Unitary equivalence to integral operators

Some equivalence classes of operators on B(H)

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.

Criteria of Unitary Equivalence of Hermitian Operators with a Degenerate Spectrum

Nonimprovable, in general, estimates of the number of necessary and sufficient conditions for two Hermitian operators to be unitarily equaivalent in a unitary space are obtained when the multiplicities of eigenvalues of operators can be more than 1. The explicit form of these conditions is given. In the Appendix the concept of conditionally functionally independent functions is given and the co...

Integral operators

1 Product measures Let (X,A , μ) be a σ-finite measure space. Then with A ⊗ A the product σalgebra and μ ⊗ μ the product measure on A ⊗A , (X ×X,A ⊗A , μ⊗ μ) is itself a σ-finite measure space. Write Fx(y) = F (x, y) and F (x) = F (x, y). For any measurable space (X ′,A ′), it is a fact that if F : X×X → X ′ is measurable then Fx is measurable for each x ∈ X and F y is measurable for each y ∈ X...