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Author: Charles Earl Rickart
Publisher:
ISBN:
Category : Algebraic functions
Languages : en
Pages : 40
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Book Description
Author: Charles Earl Rickart
Publisher:
ISBN:
Category : Algebraic functions
Languages : en
Pages : 40
Get Book Here
Book Description
Author: Charles Earl Rickart
Publisher:
ISBN:
Category : Function algebras
Languages : en
Pages : 30
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Author: Charles Earl Rickart
Publisher:
ISBN: 9783540904496
Category : Banach algebras
Languages : en
Pages : 240
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Author: Charles E. Rickart
Publisher: Springer Science & Business Media
ISBN: 1461380707
Category : Mathematics
Languages : en
Pages : 252
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Book Description
The term "function algebra" usually refers to a uniformly closed algebra of complex valued continuous functions on a compact Hausdorff space. Such Banach alge bras, which are also called "uniform algebras", have been much studied during the past 15 or 20 years. Since the most important examples of uniform algebras consist of, or are built up from, analytic functions, it is not surprising that most of the work has been dominated by questions of analyticity in one form or another. In fact, the study of these special algebras and their generalizations accounts for the bulk of the re search on function algebras. We are concerned here, however, with another facet of the subject based on the observation that very general algebras of continuous func tions tend to exhibit certain properties that are strongly reminiscent of analyticity. Although there exist a variety of well-known properties of this kind that could be mentioned, in many ways the most striking is a local maximum modulus principle proved in 1960 by Hugo Rossi [RIl]. This result, one of the deepest and most elegant in the theory of function algebras, is an essential tool in the theory as we have developed it here. It holds for an arbitrary Banaeh algebra of £unctions defined on the spectrum (maximal ideal space) of the algebra. These are the algebras, along with appropriate generalizations to algebras defined on noncompact spaces, that we call "natural func tion algebras".
Author: S.H. Kulkarni
Publisher: CRC Press
ISBN: 1000105636
Category : Mathematics
Languages : en
Pages : 201
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Book Description
This self-contained reference/text presents a thorough account of the theory of real function algebras. Employing the intrinsic approach, avoiding the complexification technique, and generalizing the theory of complex function algebras, this single-source volume includes: an introduction to real Banach algebras; various generalizations of the Stone-Weierstrass theorem; Gleason parts; Choquet and Shilov boundaries; isometries of real function algebras; extensive references; and a detailed bibliography.;Real Function Algebras offers results of independent interest such as: topological conditions for the commutativity of a real or complex Banach algebra; Ransford's short elementary proof of the Bishop-Stone-Weierstrass theorem; the implication of the analyticity or antianalyticity of f from the harmonicity of Re f, Re f(2), Re f(3), and Re f(4); and the positivity of the real part of a linear functional on a subspace of C(X).;With over 600 display equations, this reference is for mathematical analysts; pure, applied, and industrial mathematicians; and theoretical physicists; and a text for courses in Banach algebras and function algebras.
Author: T.V. Tonev
Publisher: Elsevier
ISBN: 0080872832
Category : Mathematics
Languages : en
Pages : 313
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Book Description
Treated in this volume are selected topics in analytic &Ggr;-almost-periodic functions and their representations as &Ggr;-analytic functions in the big-plane; n-tuple Shilov boundaries of function spaces, minimal norm principle for vector-valued functions and their applications in the study of vector-valued functions and n-tuple polynomial and rational hulls. Applications to the problem of existence of n-dimensional complex analytic structures, analytic &Ggr;-almost-periodic structures and structures of &Ggr;-analytic big-manifolds respectively in commutative Banach algebra spectra are also discussed.
Author: Andrew Browder
Publisher:
ISBN:
Category : Algebraic functions
Languages : en
Pages : 294
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Author: T.I. Gaisin
Publisher:
ISBN:
Category :
Languages : en
Pages : 4
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Book Description
Let be a finite-dimensional local commutative algebra over , dim. In this work we consider compact manifolds over , and prove that the real part of an -differentiable function is constant. Also we find estimates for the dimensions of some spaces of 1-form.
Author: Frank T. Birtel
Publisher:
ISBN:
Category : Function algebras
Languages : en
Pages : 376
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Book Description
These Proceedings contain articles based on the invited addresses, submitted abstracts, and informal discussions at the International Symposium on Function Algebras held at Tulane University during April 19-24, 1965, under the joint sponsorship of the National Science Foundation (Contract No. GP-3438) and the Office of Naval Research (Contract No. NRO43-326). Research problems which appear in the Appendix were formulated and discussed on the final day of the Symposium. The term Function Algebras appearing in the title is used in its general, not its technical sense. Perhaps the more generic usage, Algebras of Functions, is advisable, but it seems pedantic to insist upon this fine semantic distinction. Thus the reader is cautioned. Within a given article, Function Algebra frequently means sup norm algebra or uniform algebra: a uniformly closed separating subalgebra of the continuous complex valued functions with 1 on a compact Hausdorff space. In titles the term is frequently used to indicate any algebra which consists of functions.
Author: Kenneth P. Bogart
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 536
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Book Description
