Abstract. Let T be a p-hyponormal operator on a Hilbert space with polar decomposition T = U |T | and let T = |T | t U |T | r−t for r > 0 and r ≥ t ≥ 0. We study order and spectral properties of T . In particular we refine recent Furuta's result on p-hyponormal operators.
We consider A and B canonically embedded in their enveloping W*algebras A** and B**, so that A ® B is contained in v4** ® B** canonically. Let C " and D ~ be the weak closures of C and D. Theorem. With the above situation, if F(C, D) strictly contains C ® D and there exist projections of norm one from A** and B** onto C~ and D~, respectively, then (A
Abstract. The purpose of this paper is to introduce mosaics and principal functions of p-hyponormal operators and give a trace formula. Also we introduce p-nearly normal operators and give trace formulae for them.
We obtain a Cartesian form of Putnam's inequality for doubly commuting hyponormal n-tuples, and we establish new relations between the Taylor and Xia spectra of such n-tuples. ≤ 2 π K · m(σ(H)),where σ(H) is the spectrum of H and m is Lebesgue measure on the real line. This inequality has been extended in several ways. In the case of a single operator, it was generalized to p-hyponormal operators in [4] and to log-hyponormal operators in [12], while a trace estimate for p-hyponormal operators was obtained in [8]. For several operators, D. Xia introduced and studied hyponormal and semi-hyponormal n-tuples, and obtained preliminary versions of Putnam's inequality (cf.[16] and [17]). M. Chō and T. Huruya extended these results to p-hyponormal tuples ([5]), and recently Duggal did so to the class of doubly commuting n-tuples of p-hyponormal operators *
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.