Extremal Structure in Operator Spaces

Subspace structure of some operator and Banach spaces

We construct a family of separable Hilbertian operator spaces, such that the relation of complete isomorphism between the subspaces of each member of this family is complete Kσ . We also investigate some interesting properties of completely unconditional bases of the spaces from this family. In the Banach space setting, we construct a space for which the relation of isometry of subspaces is equ...

The Libera operator on Dirichlet spaces

In this paper, we consider the boundedness of the Libera operator on Dirichlet spaces in terms of the Schur test. Moreover, we get its point spectrum and norm.

Operator-valued bases on Hilbert spaces

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

Operator convexity in Krein spaces

We introduce the notion of Krein-operator convexity in the setting of Krein spaces. We present an indefinite version of the Jensen operator inequality on Krein spaces by showing that if (H , J) is a Krein space, U is an open set which is symmetric with respect to the real axis such that U ∩ R consists of a segment of real axis and f is a Kreinoperator convex function on U with f(0) = 0, then f(...

What are operator spaces ? Operator algebra group