PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Studia Mathematica

2009 | 194 | 1 | 91-104
Tytuł artykułu

### The joint essential numerical range of operators: convexity and related results

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let W(A) and $W_{e}(A)$ be the joint numerical range and the joint essential numerical range of an m-tuple of self-adjoint operators A = (A₁, ..., Aₘ) acting on an infinite-dimensional Hilbert space. It is shown that $W_{e}(A)$ is always convex and admits many equivalent formulations. In particular, for any fixed i ∈ {1, ..., m}, $W_{e}(A)$ can be obtained as the intersection of all sets of the form
$cl(W(A₁, ..., A_{i+1}, A_{i} + F, A_{i+1}, ..., Aₘ))$,
where F = F* has finite rank. Moreover, the closure cl(W(A)) of W(A) is always star-shaped with the elements in $W_{e}(A)$ as star centers. Although cl(W(A)) is usually not convex, an analog of the separation theorem is obtained, namely, for any element d ∉ cl(W(A)), there is a linear functional f such that f(d) > sup{f(a): a ∈ cl(W(Ã))}, where Ã is obtained from A by perturbing one of the components $A_{i}$ by a finite rank self-adjoint operator. Other results on W(A) and $W_{e}(A)$ extending those on a single operator are obtained.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
91-104
Opis fizyczny
Daty
wydano
2009
Twórcy
autor
• Department of Mathematics, The College of William and Mary, Williamsburg, VA 23185, U.S.A.
autor
• Department of Mathematics, Iowa State University, Ames, IA 50011, U.S.A.
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory