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Isomorphisms of some reflexive algebras

100%

Li J., Pan Z.

Studia Mathematica

2008

tom 187

nr 1

95-100

Suppose ℒ₁ and ℒ₂ are subspace lattices on complex separable Banach spaces X and Y, respectively. We prove that under certain lattice-theoretic conditions every isomorphism from algℒ₁ to algℒ₂ is quasi-spatial; in particular, if a subspace lattice ℒ of a complex separable Banach space X contains a sequence $E_{i}$ such that $(E_{i})₋ ≠ X$, $E_{i} ⊆ E_{i+1}$, and $ ⋁_{i=1}^{∞} E_{i} = X$ then every automorphism of algℒ is quasi-spatial.

Mappings on some reflexive algebras characterized by action on zero products or Jordan zero products

100%

Chen Y., Li J.

Studia Mathematica

2011

tom 206

nr 2

121-134

Let 𝓛 be a subspace lattice on a Banach space X and let δ: Alg𝓛 → B(X) be a linear mapping. If ⋁ {L ∈ 𝓛 : L₋ ⊉ L}= X or ⋁ {L₋ : L ∈ 𝓛, L₋ ⊉ L} = (0), we show that the following three conditions are equivalent: (1) δ(AB) = δ(A)B + Aδ(B) whenever AB = 0; (2) δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) whenever AB + BA = 0; (3) δ is a generalized derivation and δ(I) ∈ (Alg𝓛)'. If ⋁ {L ∈ 𝓛 : L₋ ⊉ L} = X or ⋁ {L₋ : L ∈ 𝓛, L₋ ⊉ L} = (0) and δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) whenever AB = 0, we show that δ is a generalized derivation and δ(I)A ∈ (Alg𝓛)' for every A ∈ Alg𝓛. We also prove that if ⋁ {L ∈ 𝓛 : L₋ ⊉ L} = X and ⋁ {L₋ : L ∈ 𝓛, L₋ ⊉ L} = (0), then δ is a local generalized derivation if and only if δ is a generalized derivation.

Ograniczanie wyników

2 Studia Mathematica

2 Li J.

1 Chen Y.

1 Pan Z.

1 2011

1 2008

Wyniki wyszukiwania

Isomorphisms of some reflexive algebras

Mappings on some reflexive algebras characterized by action on zero products or Jordan zero products