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MARC 21

Banach Space Complexes
Tag	Description
020	$a9789401103756$9978-94-011-0375-6
082	$a515.724$223
099	$aOnline resource: Springer
245	$aBanach Space Complexes$h[EBook] /$cedited by Cǎlin-Grigore Ambrozie, Florian-Horia Vasilescu.
260	$aDordrecht :$bSpringer Netherlands :$bImprint: Springer,$c1995.
300	$aV, 213 p.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aMathematics and Its Applications ;$v334
505	$aI Preliminaries -- II Semi-Fredholm complexes -- III Related topics -- Notations.
520	$aThe aim of this work is to initiate a systematic study of those properties of Banach space complexes that are stable under certain perturbations. A Banach space complex is essentially an object of the form 1 op-l oP +1 ... --+ XP- --+ XP --+ XP --+ ... , where p runs a finite or infiniteinterval ofintegers, XP are Banach spaces, and oP : Xp ..... Xp+1 are continuous linear operators such that OPOp-1 = 0 for all indices p. In particular, every continuous linear operator S : X ..... Y, where X, Yare Banach spaces, may be regarded as a complex: O ..... X ~ Y ..... O. The already existing Fredholm theory for linear operators suggested the possibility to extend its concepts and methods to the study of Banach space complexes. The basic stability properties valid for (semi-) Fredholm operators have their counterparts in the more general context of Banach space complexes. We have in mind especially the stability of the index (i.e., the extended Euler characteristic) under small or compact perturbations, but other related stability results can also be successfully extended. Banach (or Hilbert) space complexes have penetrated the functional analysis from at least two apparently disjoint directions. A first direction is related to the multivariable spectral theory in the sense of J. L.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aAmbrozie, Cǎlin-Grigore.$eeditor.
700	$aVasilescu, Florian-Horia.$eeditor.
710	$aSpringerLink (Online service)
830	$aMathematics and Its Applications ;$v334
856	$uhttp://dx.doi.org/10.1007/978-94-011-0375-6