Back to Search
Start Over
The Drazin spectrum of tensor product of Banach algebra elements and elementary operators
- Publication Year :
- 2014
-
Abstract
- Given unital Banach algebras $A$ and $B$ and elements $a\in A$ and $b\in B$, the Drazin spectrun of $a\otimes b\in A\overline{\otimes} B$ will be fully characterized, where $A\overline{\otimes} B$ is a Banach algebra that is the completion of $A\otimes B$ with respect to a uniform crossnorm. To this end, however, first the isolated points of the spectrum of $a\otimes b\in A\overline{\otimes} B$ need to be characterized. On the other hand, given Banach spaces $X$ and $Y$ and Banach space operators $S\in L(X)$ and $T\in L(Y)$, using similar arguments the Drazin spectrum of $\tau_{ST}\in L(L(Y,X))$, the elementary operator defined by $S$ and $T$, will be fully characterized.<br />Comment: 12 pages, original research article
- Subjects :
- Pure mathematics
Mathematics::Functional Analysis
Algebra and Number Theory
Approximation property
Mathematics::Operator Algebras
Spectrum (functional analysis)
Eberlein–Šmulian theorem
Finite-rank operator
Banach manifold
Compact operator
Functional Analysis (math.FA)
Mathematics - Functional Analysis
Mathematics::K-Theory and Homology
Mathematics::Quantum Algebra
Banach algebra
FOS: Mathematics
C0-semigroup
Mathematics
Primary 47A10, Secondary 46H05, 47B49
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....11bd21028496ed0c615948f78657d62b