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Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A 1 TA 2 −1 and ϕ(T) = A 2 TA 1 −1 for some bijective bounded linear operators A 1; A 2 of X onto Y, or of the form φ(T) = B 1 T*B 2 −1 and ϕ(T) = B 2 T*B −1 for some...

A Note on a Paper by W.J. Ricker and H.H. Schaefer.

Ben de Pagter (1990)

Mathematische Zeitschrift

A remark on the d-characteristic and the $d_{Ξ}$ -characteristic of linear operators in a Banach space

Štefan Schwabik (1973)

Studia Mathematica

A remark on the multipliers on spaces of Weak Products of functions

Stefan Richter, Brett D. Wick (2016)

Concrete Operators

If H denotes a Hilbert space of analytic functions on a region Ω ⊆ Cd , then the weak product is defined by [...] We prove that if H is a first order holomorphic Besov Hilbert space on the unit ball of Cd , then the multiplier algebras of H and of H ⊙ H coincide.

Additivity of maps on triangular algebras.

Cheng, Xuehan, Jing, Wu (2008)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Algebra isomorphisms between standard operator algebras

Thomas Tonev, Aaron Luttman (2009)

Studia Mathematica

If X and Y are Banach spaces, then subalgebras ⊂ B(X) and ⊂ B(Y), not necessarily unital nor complete, are called standard operator algebras if they contain all finite rank operators on X and Y respectively. The peripheral spectrum of A ∈ is the set $σ_{π} (A) = λ \in σ (A) : | λ | = m a x_{z \in σ (A)} | z |$ of spectral values of A of maximum modulus, and a map φ: → is called peripherally-multiplicative if it satisfies the equation $σ_{π} (φ (A) \circ φ (B)) = σ_{π} (A B)$ for all A,B ∈ . We show that any peripherally-multiplicative and surjective map φ: → , neither assumed to be linear nor...

Algebraic and essentially algebraic composition operators on C(X).

Albrecht Böttcher, Harald Heidler (1995)

Aequationes mathematicae

Algebraic generation of B(X) by two subalgebras with square zero

W. Żelazko (1988)

Studia Mathematica

Algebraic isomorphisms and Jordan derivations of 𝒥-subspace lattice algebras

Fangyan Lu, Pengtong Li (2003)

Studia Mathematica

It is shown that every algebraic isomorphism between standard subalgebras of 𝒥-subspace lattice algebras is quasi-spatial and every Jordan derivation of standard subalgebras of 𝒥-subspace lattice algebras is an additive derivation. Also, it is proved that every finite rank operator in a 𝒥-subspace lattice algebra can be written as a finite sum of rank one operators each belonging to that algebra. As an additional result, a multiplicative bijection of a 𝒥-subspace lattice algebra onto an arbitrary...

An Operator Ideal in Connection with Gaussian Measures and Applications to Nuclearity of Integral Operators.

Thomas Kühn (1981)

Mathematische Annalen

Arens Semi-Regular Banach Algebras.

Michael Grosser (1984)

Monatshefte für Mathematik

Arens-regularity of algebras arising from tensor norms.

Daws, Matthew (2007)

The New York Journal of Mathematics [electronic only]

Asymptotic products and enlargibility of Banach-Lie algebras.

Beltiţă, Daniel (2004)

Journal of Lie Theory

Automorphisms of the algebra of operators in $^{p}$ preserving conditioning

Ryszard Jajte (2010)

Colloquium Mathematicae

Let α be an isometric automorphism of the algebra $_{p}$ of bounded linear operators in $^{p} [0, 1]$ (p ≥ 1). Then α transforms conditional expectations into conditional expectations if and only if α is induced by a measure preserving isomorphism of [0, 1].

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