On totally paranormal operators

On Quasi ∗-paranormal Operators

An operator T ∈ B(H) is called quasi ∗-paranormal if ||T ∗Tx||2 ≤ ||T x|||Tx|| for all x ∈ H. If μ is an isolated point of the spectrum of T , then the Riesz idempotent E of T with respect to μ is defined by

Topological Properties of Paranormal Operators on Hilbert Space

Let B(H) be the set of all bounded endomorphisms (operators) on the complex Hubert space H. T € B(H) is paranormal if \\(T — z/) || = l/d(z, cr(T)) for all z £ cr(T) where d(z, cr(T)) is the distance from z to cr(T), the spectrum of T. If J is the set of all paranormal operators on H, then J contains the normal operators, JÍ, and the hyponormal operators; and J is contained in JL, the set of al...

Weyl’s Theorem for Algebraically Paranormal Operators

Let T be an algebraically paranormal operator acting on Hilbert space. We prove : (i) Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T )); (ii) a-Browder’s theorem holds for f(S) for every S ≺ T and f ∈ H(σ(S)); (iii) the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T . Mathematics Subject Classification (2000). Primary 47A10, 4...

Semi-t-operators on a finite totally ordered set

Elliptic operators of totally characteristic type

This paper contains proofs of most of the results announced in [9], together with some further developments. The basic analytic question addressed here concerns the mapping properties, on the natural Sobolev spaces, of elliptically totally characteristic pseudodifferential operators, on a compact C∞ manifold with boundary. The ring, Ψb (X), of such operators was described in detail in [8] and i...