Let A be a bounded linear operator acting on infinite dimensional separable Hilbert space H. Browder’s theorem and a-Browder’s theorem are related to an important property which has a leading role on local spectral theory: the single valued extension property see the recent monograph by Laursen and Neumann [19]. The study of operators satisfying Browder’s theorem is of significant interest, and...

In this article, we characterize absolutely norm attaining normal operators in terms of the essential spectrum. Later prove a structure theorem for hyponormal (or AN -operators short) and deduce conditions normality operator.

If T is an operator on a Hubert space %, this paper gives necessary and sufficient conditions on 7" such that C*(T), the C*-algebra generated by T, is generated by a unilateral shift of some multiplicity. This result is then specialized to the cases in which T is a hyponormal or subnormal operator. In particular, it is shown how to prove a recent conjecture of C. R. Putnam as a consequence of o...

We characterize joint k-hyponormality for 2-variable weighted shifts. Using this characterization we construct a family of examples which establishes and illustrates the gap between k-hyponormality and (k+1)-hyponormality for each k ≥ 1. As a consequence, we obtain an abstract solution to the Lifting Problem for Commuting Subnormals. 1. Notation and Preliminaries The Lifting Problem for Commuti...

It is well known that for multipliers f of the Drury-Arveson space H n, ‖f‖∞ does not dominate the operator norm of Mf . We show that in general ‖f‖∞ does not even dominate the essential norm of Mf . A consequence of this is that there exist multipliers f of H n for which Mf fails to be essentially hyponormal, i.e., if K is any compact, self-adjoint operator, then the inequality M∗ f Mf −MfM f ...

The weighted Cesáro operator Ch in ` (h)-spaces is investigated in terms of several concepts of normality, where h denotes a positive discrete measure on N0. We classify exactly those h for which Ch is hyponormal. Two examples related to the Haar measures of orthogonal polynomials are discussed. We show that the Cesáro operator is not always paranormal. Furthermore, we prove that the Cesáro ope...