Derivations of certain operator algebras.

Li, Jiankui; Pendharkar, Hemant

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Real structure in unital separable simple $C^{*}$ -algebras with tracial rank zero and with a unique tracial state.

Stacey, P.J. (2006)

The New York Journal of Mathematics [electronic only]

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Finite-rank intermediate Hankel operators on the Bergman space.

Nakazi, Takahiko, Osawa, Tomoko (2001)

International Journal of Mathematics and Mathematical Sciences

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The decomposability of operators relative to two subspaces

A. Katavolos, M. Lambrou, W. Longstaff (1993)

Studia Mathematica

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Let M and N be nonzero subspaces of a Hilbert space H satisfying M ∩ N = {0} and M ∨ N = H and let T ∈ ℬ(H). Consider the question: If T leaves each of M and N invariant, respectively, intertwines M and N, does T decompose as a sum of two operators with the same property and each of which, in addition, annihilates one of the subspaces? If the angle between M and N is positive the answer is affirmative. If the angle is zero, the answer is still affirmative for finite rank operators but...

Operators preserving ideals in C*-algebras

V. Shul'Man (1994)

Studia Mathematica

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The aim of this paper is to prove that derivations of a C*-algebra A can be characterized in the space of all linear continuous operators T : A → A by the conditions T(1) = 0, T(L∩R) ⊂ L + R for any closed left ideal L and right ideal R. As a corollary we get an extension of the result of Kadison [5] on local derivations in W*-algebras. Stronger results of this kind are proved under some additional conditions on the cohomologies of A.

Compactness conditions for elementary operators

Matej Brešar, Yuri V. Turovskii (2007)

Studia Mathematica

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Various topics concerning compact elementary operators on Banach algebras are studied: their ranges, their coefficients, and the structure of algebras having nontrivial compact elementary operators. In the first part of the paper we consider separately elementary operators of certain simple types. In the second part we obtain our main results which deal with general elementary operators.

Operators in finite distributive subspace lattices II

N. Spanoudakis (1994)

Studia Mathematica

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In a previous paper we gave an example of a finite distributive subspace lattice ℒ on a Hilbert space and a rank two operator of Algℒ that cannot be written as a finite sum of rank one operators from Algℒ. The lattice ℒ was a specific realization of the free distributive lattice on three generators. In the present paper, which is a sequel to the aforementioned one, we study Algℒ for the general free distributive lattice with three generators (on a normed space). Necessary and sufficient...

Finite rank operators in Jacobson radical $ℛ_{𝒩 \otimes ℳ}$

Zhe Dong (2006)

Czechoslovak Mathematical Journal

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In this paper we investigate finite rank operators in the Jacobson radical $ℛ_{𝒩 \otimes ℳ}$ of $A l g (𝒩 \otimes ℳ)$ , where $𝒩$ , $ℳ$ are nests. Based on the concrete characterizations of rank one operators in $A l g (𝒩 \otimes ℳ)$ and $ℛ_{𝒩 \otimes ℳ}$ , we obtain that each finite rank operator in $ℛ_{𝒩 \otimes ℳ}$ can be written as a finite sum of rank one operators in $ℛ_{𝒩 \otimes ℳ}$ and the weak closure of $ℛ_{𝒩 \otimes ℳ}$ equals $A l g (𝒩 \otimes ℳ)$ if and only if at least one of $𝒩$ , $ℳ$ is continuous.

Notes on a class of simple C*-algebras with real rank zero.

Kenneth R. Goodearl (1992)

Publicacions Matemàtiques

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A construction method is presented for a class of simple C*-algebras whose basic properties -including their real ranks- can be computed relatively easily, using linear algebra. A numerival invariant attached to the construction determines wether a given algebra has real rank 0 or 1. Moreover, these algebras all have stable rank 1, and each nonzero hereditary sub-C*-algebra contains a nonzero projection, yet there are examples in which the linear span of the projections is not dense....

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

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We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.

The set of automorphisms of B(H) is topologically reflexive in B(B(H))

Lajos Molnár (1997)

Studia Mathematica

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The aim of this paper is to prove the statement announced in the title which can be reformulated in the following way. Let H be a separable infinite-dimensional Hilbert space and let Φ: B(H) → B(H) be a continuous linear mapping with the property that for every A ∈ B(H) there exists a sequence $(Φ_{n})$ of automorphisms of B(H) (depending on A) such that $Φ (A) = l i m_{n} Φ_{n} (A)$ . Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).

On isomorphisms of standard operator algebras

Lajos Molnár (2000)

Studia Mathematica

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We show that between standard operator algebras every bijective map with a certain multiplicativity property related to Jordan triple isomorphisms of associative rings is automatically additive.