FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1505196222> ?p ?o ?g. }

• W1505196222 endingPage "147" @default.
• W1505196222 startingPage "129" @default.
• W1505196222 abstract "There are a number of spectra studied in literature which do not fit into the axiomatic theory of Żelazko. This paper is an attempt to give an axiomatic theory for these spectra which, apart from the usual types of spectra, like one-sided, approximate point or essential spectra, include also the local spectra, the Browder spectrum and various versions of the Apostol spectrum (studied under various names, e.g. regular, semi-regular or essentially semi-regular). I. Basic properties of regularities The axiomatic theory of spectrum was introduced by W. Żelazko [21], see also S lodkowski and Żelazko [17]. He gave a classification of various types of spectra defined for commuting n-tuples of elements of a Banach algebra. The most important notion is that of subspectrum. All algebras in this paper are complex and unital. Denote by Inv(A) the set of all invertible elements in a Banach algebra A and by σ(a) = {λ ∈ C, a− λ / ∈ Inv(A)} the ordinary spectrum of an element a ∈ A. The spectral radius of a ∈ A will be denoted by r(a). Definition 1.1. Let A be a Banach algebra. A subspectrum σ in A is a mapping which assigns to every n-tuple (a1, . . . , an) of mutually commuting elements of A a non-empty compact subset σ(a1, . . . , an) ⊂ C such that (1) σ(a1, . . . , an) ⊂ σ(a1)× · · · × σ(an), (2) σ(p(a1, . . . , an)) = p(σ(a1, . . . , an)) for every commuting a1, . . . , an ∈ A and every polynomial mapping p = (p1, . . . , pm) : C → C. This notion has proved to be quite useful since it includes for example the left (right) spectrum, the left (right) approximate point spectrum, the Harte (= the union of the left and right) spectrum, the Taylor spectrum and various essential spectra. However, there are also many examples of spectrum, usually defined only for single elements of A, which are not covered by the axiomatic theory of Żelazko. The aim of this paper is to give an axiomatic description of such spectra. Instead of describing a spectrum, it is possible to describe equivalently the set of regular elements. Definition 1.2. Let A be a Banach algebra. A non-empty subset R of A is called a regularity if (1) if a ∈ A and n ∈ N then a ∈ A ⇔ a ∈ A, (2) if a, b, c, d are mutually commuting elements of A and ac + bd = 1A, then ab ∈ R ⇔ a ∈ R and b ∈ R." @default.
• W1505196222 created "2016-06-24" @default.
• W1505196222 creator A5048945258 @default.
• W1505196222 creator A5083530338 @default.
• W1505196222 date "1996-01-01" @default.
• W1505196222 modified "2023-10-14" @default.
• W1505196222 title "On the axiomatic theory of spectrum II" @default.
• W1505196222 cites W1564607148 @default.
• W1505196222 cites W1573764128 @default.
• W1505196222 cites W1575147392 @default.
• W1505196222 cites W1576177157 @default.
• W1505196222 cites W1661659201 @default.
• W1505196222 cites W1956024869 @default.
• W1505196222 cites W1966466703 @default.
• W1505196222 cites W1977614362 @default.
• W1505196222 cites W1984914884 @default.
• W1505196222 cites W1986875623 @default.
• W1505196222 cites W2002316469 @default.
• W1505196222 cites W2007707831 @default.
• W1505196222 cites W2009401523 @default.
• W1505196222 cites W2014965333 @default.
• W1505196222 cites W2022665730 @default.
• W1505196222 cites W2032925154 @default.
• W1505196222 cites W2039779271 @default.
• W1505196222 cites W2056870693 @default.
• W1505196222 cites W2059208530 @default.
• W1505196222 cites W2061160079 @default.
• W1505196222 cites W2074884170 @default.
• W1505196222 cites W2082843210 @default.
• W1505196222 cites W212161842 @default.
• W1505196222 cites W2162585625 @default.
• W1505196222 cites W2228298730 @default.
• W1505196222 cites W2523986151 @default.
• W1505196222 cites W3048051339 @default.
• W1505196222 cites W194918426 @default.
• W1505196222 doi "https://doi.org/10.4064/sm-119-2-129-147" @default.
• W1505196222 hasPublicationYear "1996" @default.
• W1505196222 type Work @default.
• W1505196222 sameAs 1505196222 @default.
• W1505196222 citedByCount "110" @default.
• W1505196222 countsByYear W15051962222012 @default.
• W1505196222 countsByYear W15051962222013 @default.
• W1505196222 countsByYear W15051962222014 @default.
• W1505196222 countsByYear W15051962222015 @default.
• W1505196222 countsByYear W15051962222016 @default.
• W1505196222 countsByYear W15051962222017 @default.
• W1505196222 countsByYear W15051962222018 @default.
• W1505196222 countsByYear W15051962222019 @default.
• W1505196222 countsByYear W15051962222020 @default.
• W1505196222 countsByYear W15051962222021 @default.
• W1505196222 countsByYear W15051962222022 @default.
• W1505196222 countsByYear W15051962222023 @default.
• W1505196222 crossrefType "journal-article" @default.
• W1505196222 hasAuthorship W1505196222A5048945258 @default.
• W1505196222 hasAuthorship W1505196222A5083530338 @default.
• W1505196222 hasBestOaLocation W15051962221 @default.
• W1505196222 hasConcept C121332964 @default.
• W1505196222 hasConcept C125773388 @default.
• W1505196222 hasConcept C136119220 @default.
• W1505196222 hasConcept C144237770 @default.
• W1505196222 hasConcept C156778621 @default.
• W1505196222 hasConcept C167729594 @default.
• W1505196222 hasConcept C199343813 @default.
• W1505196222 hasConcept C202444582 @default.
• W1505196222 hasConcept C2524010 @default.
• W1505196222 hasConcept C2777686260 @default.
• W1505196222 hasConcept C33923547 @default.
• W1505196222 hasConcept C62520636 @default.
• W1505196222 hasConcept C71924100 @default.
• W1505196222 hasConceptScore W1505196222C121332964 @default.
• W1505196222 hasConceptScore W1505196222C125773388 @default.
• W1505196222 hasConceptScore W1505196222C136119220 @default.
• W1505196222 hasConceptScore W1505196222C144237770 @default.
• W1505196222 hasConceptScore W1505196222C156778621 @default.
• W1505196222 hasConceptScore W1505196222C167729594 @default.
• W1505196222 hasConceptScore W1505196222C199343813 @default.
• W1505196222 hasConceptScore W1505196222C202444582 @default.
• W1505196222 hasConceptScore W1505196222C2524010 @default.
• W1505196222 hasConceptScore W1505196222C2777686260 @default.
• W1505196222 hasConceptScore W1505196222C33923547 @default.
• W1505196222 hasConceptScore W1505196222C62520636 @default.
• W1505196222 hasConceptScore W1505196222C71924100 @default.
• W1505196222 hasIssue "2" @default.
• W1505196222 hasLocation W15051962221 @default.
• W1505196222 hasLocation W15051962222 @default.
• W1505196222 hasOpenAccess W1505196222 @default.
• W1505196222 hasPrimaryLocation W15051962221 @default.
• W1505196222 hasRelatedWork W1584952351 @default.
• W1505196222 hasRelatedWork W2054299810 @default.
• W1505196222 hasRelatedWork W2074760288 @default.
• W1505196222 hasRelatedWork W2106357750 @default.
• W1505196222 hasRelatedWork W2116374711 @default.
• W1505196222 hasRelatedWork W2163307967 @default.
• W1505196222 hasRelatedWork W2323135783 @default.
• W1505196222 hasRelatedWork W2702281908 @default.
• W1505196222 hasRelatedWork W3122092647 @default.
• W1505196222 hasRelatedWork W2127270425 @default.
• W1505196222 hasVolume "119" @default.

• next