A class of hyponormal operators and weak*-continuity of hermitian operators
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In this article, a class of *-hyponormal operators, called subnormal operators on a Hilbert space, were studied and a generalized Fuglede-Putnam theorem was proved for these operators.Abstract:
We will first in this paper consider a class of hyponormal operators which we call *-hyponormal operators. We give an example of a hyponormal operator which is not *-hyponormal. It follows from a theorem of Ackermans, van Eijndhoven and Martens [1] that subnormal operators on a Hilbert space are *-hyponormal. We prove a generalized Fuglede--Putnam theorem and some other results for these operators. We will also prove some results on the following problem which was mentioned in [4]:read more
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Skew exactness and range-kernel orthogonality II
TL;DR: The Fuglede property extends to ∗ -hyponormal Banach algebra elements and certain Banach elements are approximated by self-commutators as discussed by the authors, which is a special case of the selfcommutation property.
Skew exactness and range-kernel orthogonality III
TL;DR: In this article, a range-kernel orthogonality for elementary operators defining Hankel and Toeplitz operators is given for the class of elementary operators defined in this paper.
Journal ArticleDOI
On the Single-Valued Extension Property of Hyponormal Operators on Banach Spaces
Muneo Chō,Injo Hur,Ji Eun Lee +2 more
TL;DR: In this article, the authors studied the single-valued extension property of hyponormal operators on Banach spaces and proved that if a bounded linear operator T on the Banach space has the property (II) or the property(I $$')$$� (see Definition 2.3).
References
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Book
Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras
F. F. Bonsall,J. Duncan +1 more
Abstract: 1. Numerical range in unital normed algebras 2. Hermitian elements of a complex unital Banach algebra 3. Operators 4. Some recent developments.
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On relatively disjoint families of measures, with some applications to Banach space theory
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The second conjugate space of a Banach algebra as an algebra
Paul Civin,Bertram Yood +1 more