 PreliminariesCarlos S. Kubrusly
Chapter Chapter 0 in An Introduction to Models and Decompositions in Operator Theory, 1997, pp 1-22 from Springer Abstract: Abstract This chapter summarizes the background material required for reading this book. Its purpose is twofold: notation and basic results. We shall try to stick to the usual notation of operator theory literature as far as possible or convenient. In particular, for a given Hubert space H, the sesquilinear form (linear in the first argument) ‹•; •›:H × H → C will stand for inner product in H. We shall not distinguish notation for norms. Thus ∥ • ∥ will denote not only the norm generated by the inner product in H (i.e. ∥x∥2 = ‹x; x› for all x ∈ H) but operator norm as well. By “basic results” we simply mean those well-known theorems that will be needed in the sequel, and only those. We shall not, in this chapter, make any attempt to prove all of them or point out a reference to each of them, but we shall refer the reader to current literature. Thus (almost) everything that is summarized here can be found, for instance, in [3, 4, 6, 7, 16, 21, 32, 62, 75, 78 and 91]. References to subsequent chapters (e.g. [17, 24, 29, 39, 40, 72 and 87]) also contain a good deal of such background material. Keywords: Hilbert Space; Invariant Subspace; Direct Summand; Partial Isometry; Linear Manifold (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1998-9_1 Ordering information: This item can be ordered from DOI: 10.1007/978-1-4612-1998-9_1 Access Statistics for this chapter More chapters in Springer Books from Springer |
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