zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Samuel multiplicity and the structure of semi-Fredholm operators. (English) Zbl 1070.47007

In this paper, the shift Samual multiplicity, denoted s mul (T), and the backward shift Samual multiplicity, denoted bs mul (T), are introduced for any semi-Fredholm operator T on a separable complex Hilbert space H:

s mul (T)=lim t (dim(H/T k (H))/k),
bs mul (T)=lim t (dim(ker(T k )))/k)·

These numerical invariants refining the Fredholm index can be regarded as stabilized dimensions of the cokernel H/T(H) and kernel ker(T), respectively. A geometric interpretation of s mul (T) and bs mul (T) leads to a local version of Apostol’s triangular representation theorem and to Gohberg’s punctured neighborhood theorem. Banach space operators are also considered.

47A53(Semi-)Fredholm operators; index theories
47A13Several-variable spectral theory
46H25Normed modules and Banach modules, topological modules