Operator theory on quaternionic Hilbert spaces

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-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 dene the concepts of bessel, hilbert ov-basis and obt...

OPERATOR THEORY ON HILBERT SPACE Class notes

Interpolation between Hilbert , Banach and Operator spaces

Motivated by a question of Vincent Lafforgue, we study the Banach spaces X satisfying the following property: there is a function ε → ∆ X (ε) tending to zero with ε > 0 such that every operator T : L 2 → L 2 with T ≤ ε that is simultaneously contractive (i.e. of norm ≤ 1) on L 1 and on L ∞ must be of norm ≤ ∆ X (ε) on L 2 (X). We show that ∆ X (ε) ∈ O(ε α) for some α > 0 iff X is isomorphic to ...

Hilbert spaces expanded with a unitary operator

We study Hilbert spaces expanded with a unitary operator with a countable spectrum. We show the theory of such a structure is ω-stable and has quantifier elimination.