Displaying similar documents to “How to solve an operator equation.”

Polar decomposition in Rickart C*-algebras.

Dmitry Goldstein (1995)

Publicacions Matemàtiques

Similarity:

A new proof is obtained to the following fact: a Rickart C*-algebra satisfies polar decomposition. Equivalently, matrix algebras over a Rickart C*-algebra are also Rickart C*-algebras.

Operators preserving ideals in C*-algebras

V. Shul'Man (1994)

Studia Mathematica

Similarity:

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.

Factorization of operators on C*-algebras

Narcisse Randrianantoanina (1998)

Studia Mathematica

Similarity:

Let A be a C*-algebra. We prove that every absolutely summing operator from A into 2 factors through a Hilbert space operator that belongs to the 4-Schatten-von Neumann class. We also provide finite-dimensional examples that show that one cannot replace the 4-Schatten-von Neumann class by the p-Schatten-von Neumann class for any p < 4. As an application, we show that there exists a modulus of capacity ε → N(ε) so that if A is a C*-algebra and T Π 1 ( A , 2 ) with π 1 ( T ) 1 , then for every ε >0, the...