Communications in Algebra, ISSN 0092-7872, 12/2019, Volume 47, Issue 12, pp. 5294 - 5302

Let be a triangular algebra. We show that under suitable assumptions every generalized Lie n-derivation associated with a linear map is of the form where and Δ...

triangular algebra | 15A78 | Derivation | generalized Lie n-derivation | 16W25 | Lie n-derivation | 47L35 | Maps | Algebra

triangular algebra | 15A78 | Derivation | generalized Lie n-derivation | 16W25 | Lie n-derivation | 47L35 | Maps | Algebra

Journal Article

Communications in Algebra, ISSN 0092-7872, 05/2019, Volume 47, Issue 5, pp. 1841 - 1852

Let be a 2-torsion free commutative ring with unity, X a locally finite preordered set and the incidence algebra of X over . If X consists of a finite number...

Lie triple derivation | 06A11 | Derivation | Primary 16W25 | Secondary 16W10 | 47L35 | incidence algebra | Incidence

Lie triple derivation | 06A11 | Derivation | Primary 16W25 | Secondary 16W10 | 47L35 | incidence algebra | Incidence

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 05/2019, Volume 67, Issue 5, pp. 886 - 895

Let be an arbitrary unital *-algebra over the real or complex field , and let with . Assume that is a map. It is shown that, if satisfies for each and...

skew product maps | 46J10 | 47B48 | algebras | nest algebra | Preserving problems | 47L35

skew product maps | 46J10 | 47B48 | algebras | nest algebra | Preserving problems | 47L35

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 04/2018, Volume 66, Issue 4, pp. 671 - 680

In this paper, we suppose that and are two rings, where has a unit element 1 and , we show that if every Jordan homomorphism from into is a homomorphism...

Primary: 47B48 | n-homomorphism | 47C15 | Secondary: 47L35 | n-Jordan homomorphism | Homomorphism | Jordan homomorphism | MATHEMATICS | BANACH-ALGEBRAS | Homomorphisms

Primary: 47B48 | n-homomorphism | 47C15 | Secondary: 47L35 | n-Jordan homomorphism | Homomorphism | Jordan homomorphism | MATHEMATICS | BANACH-ALGEBRAS | Homomorphisms

Journal Article

Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 2015, Volume 45, Issue 4, pp. 1357 - 1368

Let R be a commutative ring with identity and I(X, R.) the incidence algebra of a locally finite preordered set X. In this note, we characterize the...

Derivation | Jordan derivation | Incidence algebra | MATHEMATICS | AUTOMORPHISMS | TRIANGULAR MATRIX-RINGS | incidence algebra | 16W25 | 16W10 | 47L35

Derivation | Jordan derivation | Incidence algebra | MATHEMATICS | AUTOMORPHISMS | TRIANGULAR MATRIX-RINGS | incidence algebra | 16W25 | 16W10 | 47L35

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 01/2013, Volume 438, Issue 1, pp. 584 - 597

Let R be a triangular ring. The problem of describing the form of additive maps F1,F2,G1,G2:R→R satisfying functional identity F1(x)y+F2(y)x+xG2(y)+yG1(x)=0...

Functional identity | Nest algebra | Generalized inner biderivation | 16S50 | Triangular matrix ring | Commuting map | 16R60 | 47L35 | Triangular ring | MATHEMATICS, APPLIED | ALGEBRAS | MAPS | GENERALIZED BIDERIVATIONS | CENTRALIZING MAPPINGS

Functional identity | Nest algebra | Generalized inner biderivation | 16S50 | Triangular matrix ring | Commuting map | 16R60 | 47L35 | Triangular ring | MATHEMATICS, APPLIED | ALGEBRAS | MAPS | GENERALIZED BIDERIVATIONS | CENTRALIZING MAPPINGS

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 06/2017, Volume 65, Issue 6, pp. 1158 - 1170

Let be a triangular algebra and let be a nonlinear generalized Lie derivation with an associated nonlinear map f. It is showed and f are the sum of an additive...

16W25 | 47L35 | nonlinear generalized Lie derivation | Triangular algebra | generalized Lie derivation | MATHEMATICS | MAPS | RINGS | NEUMANN-ALGEBRAS | Algebra | Derivation | Nonlinearity | Additives | Commutators | Images

16W25 | 47L35 | nonlinear generalized Lie derivation | Triangular algebra | generalized Lie derivation | MATHEMATICS | MAPS | RINGS | NEUMANN-ALGEBRAS | Algebra | Derivation | Nonlinearity | Additives | Commutators | Images

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 3/2015, Volume 81, Issue 3, pp. 427 - 434

A set of operators is said to be decomposable if each finite rank operator in it can be written as a sum of finitely many rank-1 operators in it. In this note,...

Nest algebra | Primary 47L35 | Rank one operator | Analysis | Decomposability | Mathematics | Lie ideal | MATHEMATICS | Algebra

Nest algebra | Primary 47L35 | Rank one operator | Analysis | Decomposability | Mathematics | Lie ideal | MATHEMATICS | Algebra

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 9/2013, Volume 77, Issue 1, pp. 109 - 121

Let X be a Banach space of dimension > 2. We show that every local Lie derivation of B(X) is a Lie derivation, and that a map of B(X) is a 2-local Lie...

Lie derivation | 2-local lie derivation | Secondary 17B40 | Primary 47L35 | Analysis | Derivation | local lie derivation | Mathematics | MATHEMATICS | Computer science | Algebra

Lie derivation | 2-local lie derivation | Secondary 17B40 | Primary 47L35 | Analysis | Derivation | local lie derivation | Mathematics | MATHEMATICS | Computer science | Algebra

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 03/2015, Volume 63, Issue 3, pp. 534 - 553

Using the notion of the maximal left ring of quotients, our recent result on the solutions of functional identity in triangular rings is generalized....

maximal left ring of quotients | biderivation | extended centroid | 16S50 | commuting map | triangular ring | nest algebra | upper triangular matrix ring | 16R60 | functional identity | 47L35 | MATHEMATICS | ALGEBRAS | BIDERIVATIONS | MAPS | Additives | Algebra | Maps | Quotients | Images | Rings (mathematics)

maximal left ring of quotients | biderivation | extended centroid | 16S50 | commuting map | triangular ring | nest algebra | upper triangular matrix ring | 16R60 | functional identity | 47L35 | MATHEMATICS | ALGEBRAS | BIDERIVATIONS | MAPS | Additives | Algebra | Maps | Quotients | Images | Rings (mathematics)

Journal Article

Banach Journal of Mathematical Analysis, ISSN 1735-8787, 04/2016, Volume 10, Issue 2, pp. 223 - 234

Let A be a unital algebra over a number field F. A linear mapping phi from A into itself is called a Jordan-centralized mapping at a given point G is an...

Jordan centralizer | Centralizer | Non-self-adjoint operator algebra | Triangular algebra | MATHEMATICS | MATHEMATICS, APPLIED | triangular algebra | ISOMORPHISMS | centralizer | DERIVATIONS | non-self-adjoint operator algebra

Jordan centralizer | Centralizer | Non-self-adjoint operator algebra | Triangular algebra | MATHEMATICS | MATHEMATICS, APPLIED | triangular algebra | ISOMORPHISMS | centralizer | DERIVATIONS | non-self-adjoint operator algebra

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 08/2015, Volume 63, Issue 8, pp. 1693 - 1706

Let X be a complex Banach space with dimension greater than 1. Let be a subspace lattice of X with or . Assume that is a linear Lie -derivation. It is shown...

derivations | Lie derivations | 47B47 | Lie n-derivations | 47L35 | reflexive algebras | MATHEMATICS | TRIPLE DERIVATIONS | Algebra | Lattices | Images | Derivation | Subspaces | Banach space | Commutators

derivations | Lie derivations | 47B47 | Lie n-derivations | 47L35 | reflexive algebras | MATHEMATICS | TRIPLE DERIVATIONS | Algebra | Lattices | Images | Derivation | Subspaces | Banach space | Commutators

Journal Article

Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 08/2016, Volume 59, Issue 3, pp. 605 - 621

We define an equivalence relation between bimodules over maximal abelian self-adjoint algebras (MASA bimodules), which we call spatial Morita equivalence. We...

2010 Mathematics subject classification: Primary 47L35 | Secondary 47L05 | MATHEMATICS | Morita equivalence | ALGEBRAS | SUBSPACES | MASA bimodules | reflexivity | Mathematics | Lattice theory | Algebra | Homomorphisms | Operators | Equivalence | Mathematical analysis | Masa

2010 Mathematics subject classification: Primary 47L35 | Secondary 47L05 | MATHEMATICS | Morita equivalence | ALGEBRAS | SUBSPACES | MASA bimodules | reflexivity | Mathematics | Lattice theory | Algebra | Homomorphisms | Operators | Equivalence | Mathematical analysis | Masa

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 07/2015, Volume 63, Issue 7, pp. 1309 - 1331

Let be a triangular algebra over a commutative ring and be the centre of . Suppose that is an -bilinear mapping and that is a trace of . We describe the form...

triangular algebra | 15A78 | nest algebra | centralizing trace | commuting trace | Lie triple isomorphism | 47L35 | HOMOMORPHISMS | AUTOMORPHISMS | DERIVATIONS | COMMUTING TRACES | MATHEMATICS | JORDAN ISOMORPHISMS | MAPS | MAPPINGS | Algebra | Matrix algebra | Mathematical analysis | Images | Isomorphism | Mapping | Standards | Rings (mathematics)

triangular algebra | 15A78 | nest algebra | centralizing trace | commuting trace | Lie triple isomorphism | 47L35 | HOMOMORPHISMS | AUTOMORPHISMS | DERIVATIONS | COMMUTING TRACES | MATHEMATICS | JORDAN ISOMORPHISMS | MAPS | MAPPINGS | Algebra | Matrix algebra | Mathematical analysis | Images | Isomorphism | Mapping | Standards | Rings (mathematics)

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 05/2016, Volume 64, Issue 5, pp. 863 - 869

The aim of the paper is to give a condition on which every centralizing trace of a bilinear map on triangular algebras is commuting. As an application, we give...

triangular algebra | 15A78 | centralizing trace | 16W25 | commuting trace | Lie triple isomorphism | 47L35 | RINGS | UNITAL ALGEBRAS | N-DERIVATIONS | FUNCTIONAL IDENTITIES | MATHEMATICS | COMMUTING MAPS | IDEMPOTENTS | GENERALIZED MATRIX ALGEBRAS | Isomorphism | Paper | Algebra

triangular algebra | 15A78 | centralizing trace | 16W25 | commuting trace | Lie triple isomorphism | 47L35 | RINGS | UNITAL ALGEBRAS | N-DERIVATIONS | FUNCTIONAL IDENTITIES | MATHEMATICS | COMMUTING MAPS | IDEMPOTENTS | GENERALIZED MATRIX ALGEBRAS | Isomorphism | Paper | Algebra

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 4/2017, Volume 40, Issue 2, pp. 505 - 522

We consider the problem of describing the form of biderivations of a triangular ring. Our approach is based on the notion of the maximal left ring of...

Nest algebra | Derivation | Mathematics | Upper triangular matrix ring | Utumi left quotient ring | Extended centroid | 15A78 | Mathematics, general | Biderivation | 16W25 | Applications of Mathematics | Triangular ring | Maximal left ring of quotients | 47L35 | MATHEMATICS | ALGEBRAS | GENERALIZED BIDERIVATIONS | COMMUTING MAPS | Quotients | Linear algebra | Rings (mathematics)

Nest algebra | Derivation | Mathematics | Upper triangular matrix ring | Utumi left quotient ring | Extended centroid | 15A78 | Mathematics, general | Biderivation | 16W25 | Applications of Mathematics | Triangular ring | Maximal left ring of quotients | 47L35 | MATHEMATICS | ALGEBRAS | GENERALIZED BIDERIVATIONS | COMMUTING MAPS | Quotients | Linear algebra | Rings (mathematics)

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 05/2011, Volume 59, Issue 5, pp. 571 - 594

In this article, we get a complete classification of distance preserving surjective maps Φ between nest algebras acting on separable Hilbert spaces.

distance preservers | nest algebras | 47L35 | 47A30 | primary 47B49 | Distance preservers | Nest algebras | MATHEMATICS

distance preservers | nest algebras | 47L35 | 47A30 | primary 47B49 | Distance preservers | Nest algebras | MATHEMATICS

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 4/2016, Volume 10, Issue 4, pp. 783 - 794

Based on a bounded approximate version of LU decomposition, we calculate the topological stable rank of $${{\mathcal {A}}}_{{\mathcal {N}}}$$ A N , which is a...

47L75 | Operator Theory | A noncommutative version of the disc algebra | 19B10 | Analysis | Mathematics, general | Mathematics | 47L35 | Topological stable rank | MATHEMATICS | MATHEMATICS, APPLIED | Algebra

47L75 | Operator Theory | A noncommutative version of the disc algebra | 19B10 | Analysis | Mathematics, general | Mathematics | 47L35 | Topological stable rank | MATHEMATICS | MATHEMATICS, APPLIED | Algebra

Journal Article

Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 02/2015, Volume 45, Issue 1, pp. 345 - 358

Let \mathcal{L} be a \mathcal{J}-subspace lattice on a complex Banach space X and \mbox{\rm Alg\,}{\mathcal L} the associated \mathcal{J}-subspace lattice...

mathcal J-subspace lattice algebra | derivations | generalized derivations | 47B47 | 47L35 | full-derivable point

mathcal J-subspace lattice algebra | derivations | generalized derivations | 47B47 | 47L35 | full-derivable point

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 08/2012, Volume 60, Issue 8, pp. 979 - 994

Let ℛ be a commutative ring with identity, A, B be unital algebras over ℛ and M be a unital (A, B)-bimodule, which is faithful as a left A-module and also as a...

nonlinear Lie higher derivation | 16W25 | triangular algebra | 15A78 | 47L35 | MATHEMATICS | TRIPLE DERIVATIONS | MATRIX-RINGS | AUTOMORPHISMS | NEST-ALGEBRAS | Additives | Algebra | Scripts | Derivation | Nonlinearity | Mapping | Standards | Rings (mathematics)

nonlinear Lie higher derivation | 16W25 | triangular algebra | 15A78 | 47L35 | MATHEMATICS | TRIPLE DERIVATIONS | MATRIX-RINGS | AUTOMORPHISMS | NEST-ALGEBRAS | Additives | Algebra | Scripts | Derivation | Nonlinearity | Mapping | Standards | Rings (mathematics)

Journal Article

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