The unitary equivalence of compact operators

Unitary Invariants for Compact Operators

We describe in this note how the "boundary representation" technique introduced in [l ] leads to a complete classification of compact operators on Hubert spaces to unitary equivalence (Theorem 3), in terms of a sequence of invariants related to (and generalizing) the numerical range. These invariants are, we feel, vastly simpler than one might have anticipated in so general a situation. Full de...

Some equivalence classes of operators on B(H)

Weak Banach-Saks property in the space of compact operators

For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and‎ ‎a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$‎, ‎it is shown that the strong Banach-Saks-ness of all evaluation‎ ‎operators on ${mathcal M}$ is a sufficient condition for the weak‎ ‎Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in‎ ‎Y^*$‎, ‎the evaluation op...

Generalized Unitary Operators

1. Let C be the complex field and T be the unit circle { \ £ C : | \ | = 1} . For a non-negative integer m or for m = oo, let OCT) be the space of all m-times continuously differentiable functions on T. (Here we consider T as a C°°-manifold in the natural way. Thus, any / £ C m ( r ) can be identified with an m-times continuously differentiable periodic function f (6) of a real variable 0 with ...

Unitary Operators Preserving Wavelets

We characterize a special class of unitary operators that preserve orthonormal wavelets. In the process we also prove that symmetric wavelet sets cover the real line.