Note on subnormal weighted shifts

One-step extensions of subnormal 2-variable weighted shifts

A Note on Subnormal and Hyponormal Derivations

In this note we prove that if A and B∗ are subnormal operators and X is a bounded linear operator such that AX − XB is a Hilbert-Schmidt operator, then f(A)X −Xf(B) is also a Hilbert-Schmidt operator and ||f(A)X −Xf(B)||2 ≤ L ||AX −XB||2, for f belonging to a certain class of functions. Furthermore, we investigate the similar problem in the case that S, T are hyponormal operators and X ∈ L(H) i...

On Polynomially Bounded Weighted Shifts

(1) ‖p(T )‖ ≤M sup{|p(ζ)| : |ζ| = 1} ∀ polynomial p, and to be power bounded (notation T ∈ (PW)) if (1) holds for every polynomial of the special form p(ζ) = ζ where n is a positive integer. If T ∈ (PB) [resp., T ∈ (PW)], then there is a smallest number M which satisfies (1) [resp., (1) restricted]. This number will be called the polynomial bound of T [resp., the power bound of T ] and denoted ...

A Note on Weighted Composition Operators on L^p-Spaces

On Polynomially Bounded Weighted Shifts, Ii

Let T be an operator-weighted shift whose weights are 2-by-2 matrices. We say that, given > 0, T is in the -canonical form if each weight is an upper triangular matrix (aij), with 0 ≤ a11, a22 ≤ 1 and a12 6= 0 implies a11, a22 < . We generalize this concept to operator-weighted shifts whose weights are n-by-n matrices and we show that every polynomially bounded weighted shift, whose weights are...