This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis
is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern …

The book introduces spectral theory for bounded linear operators, giving a modern text for a
graduate course focusing on two basic aspects. On the one hand, the spectral theory for …

A Hilbert Space operator T is of class Q if T2* T2− 2T* T+ I is nonnegative. Every paranormal
operator is of class Q, but class-Q operators are not necessarily normaloid. It is shown that if …

It is still unknown whether the inverse of an invertible k-paranormal operator is normaloid,
and so whether a k-paranormal operator is totally hereditarily normaloid. We provide …

This is a brief introduction to Fredholm theory for Hilbert space operators organized into ten
sections. The classical partition of the spectrum into point, residual, and continuous spectra …

If T is a Hilbert space contraction, then, where A is a nonnegative contraction. The strong
limit A is a projection if and only T= G⊕ V, where G is a strongly stable contraction and V is …

Let T and S be Hilbert space operators such that Weyl's theorem holds for both of them. In
general, it does not follow that Weyl's theorem holds for the direct sum T⊕ S. We give …

A Banach space operator T∈ B (¥ cal {X}) is hereditarily polaroid, T∈(¥ cal {HP}), if the
isolated points of the spectrum of every part Tp of the operator are poles of the resolvent of …

A Banach space operator T∈ B (X) is said to be totally hereditarily normaloid, T∈ THN, if
every part of T is normaloid and every invertible part of T has a normaloid inverse. The …

Abstract If T=\left (T_1&\quad C\0&\quad T_2) ∈ B (X _1 ⊕ X _2) is a Banach space upper
triangular operator matrix with diagonal (T_1, T_2) such that T_2 is k-nilpotent for some …