Skew exactness and range-kernel orthogonality II

We record some “range-kernel orthogonality” for the elementary operators defining Hankel and Toeplitz operators.

/pdf/skew-exactness-and-range-kernel-orthogonality-iii-1kdqayx5xq.pdf

Skew exactness and range-kernel orthogonality III

In this paper, we study the single-valued extension property of hyponormal operators on Banach spaces $${\mathcal {X}}$$
 . In particular, we prove that if a bounded linear operator T on $${\mathcal {X}}$$
 has the property (II) or the property (I
 $$')$$
 (see Definition 2.3), then T has the single-valued extension property. Moreover, we show that for strictly convex (resp., smooth) $$\mathcal {{\mathcal {X}}}$$
 , if $$T\in {{\mathcal {L}}}(\mathcal {{\mathcal {X}}})$$
 is hyponormal (resp., $$\,^*$$
 -hyponormal) on $$\mathcal {{\mathcal {X}}}$$
 , then T has the single-valued extension property.

On the Single-Valued Extension Property of Hyponormal Operators on Banach Spaces

Generalizations of the Fuglede-Putnam Theorem to Banach Algebras and Spaces

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]:

/pdf/a-class-of-hyponormal-operators-and-weak-continuity-of-35j4jc39w2.pdf

Kirsti Mattila

Papers

A class of hyponormal operators and weak*-continuity of hermitian operators