Introduction to Functional Analysis: Banach Spaces and Differential Calculus.

1983 ◽  
Vol 90 (8) ◽  
pp. 579
Author(s):  
Joe Diestel ◽  
Leopoldo Nachbin
Keyword(s):  
Functional Analysis ◽  
Banach Spaces ◽  
Differential Calculus

scholarly journals Joint spectra of commuting normal operators on Banach spaces

1988 ◽  
Vol 30 (3) ◽  
pp. 339-345 ◽  
Author(s):  
Muneo Chō
Keyword(s):  
Functional Analysis ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Functional Calculus ◽  
Joint Spectrum ◽  
Normal Operators

The joint spectrum for a commuting n-tuple in functional analysis has its origin in functional calculus which appeared in J. L. Taylor's epoch-making paper [19] in 1970. Since then, many papers have been published on commuting n-tuples of operators on Hilbert spaces (for example, [3], [4], [5], [8], [9], [10], [21], [22]).

GENERALIZED p-FRAME IN SEPARABLE COMPLEX BANACH SPACES

2010 ◽  
Vol 08 (01) ◽  
pp. 133-148 ◽  
Author(s):  
XIANG-CHUN XIAO ◽  
YU-CAN ZHU ◽  
XIAO-MING ZENG
Keyword(s):  
Banach Space ◽  
Functional Analysis ◽  
Hilbert Space ◽  
Banach Spaces ◽  
Riesz Basis ◽  
Complex Banach Space ◽  
Complex Hilbert Space ◽  
The Stability

The concept of g-frame and g-Riesz basis in a complex Hilbert space was introduced by Sun.18 In this paper, we generalize the g-frame and g-Riesz basis in a complex Hilbert space to a complex Banach space. Using operators theory and methods of functional analysis, we give some characterizations of a g-frame or a g-Riesz basis in a complex Banach space. We also give a result about the stability of g-frame in a complex Banach space.

scholarly journals Non-Archimedean t-Frames and FM-Spaces

1992 ◽  
Vol 35 (4) ◽  
pp. 475-483 ◽  
Author(s):  
N. De Grande-De Kimpe ◽  
C. Perez-Garcia ◽  
W. H. Schikhof
Keyword(s):  
Functional Analysis ◽  
Banach Spaces ◽  
Type Theorem ◽  
Countable Type ◽  
Nuclear Spaces

AbstractWe generalize the notion of t-orthogonality in p-adic Banach spaces by introducing t-frames (§2). This we use to prove that a Fréchet-Montel (FM-)space is of countable type (Theorem 3.1), the non-archimedeancounterpart of a well known theorem in functional analysis over ℝ or ℂ ([6], p. 231). We obtain several characterizations of FM-spaces (Theorem 3.3) and characterize the nuclear spaces among them (§4).

Elements of Geometry of Balls in Banach Spaces

2018 ◽  
Author(s):  
Kazimierz Goebel ◽  
Stanislaw Prus
Keyword(s):  
Functional Analysis ◽  
Graduate Students ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Normed Spaces ◽  
The Subject ◽  
Basic Facts ◽  
Weak Topologies

One of the subjects of functional analysis is classification of Banach spaces depending on various properties of the unit ball. The need of such considerations comes from a number of applications to problems of mathematical analysis. The list of subjects contains: differential calculus in normed spaces, approximation theory, weak topologies and reflexivity, general theory of convexity and convex functions, metric fixed point theory, and others. The aim of this book is to present basic facts from this field. It is addressed to advanced undergraduate and graduate students interested in the subject. For some it may result in further interest, a continuation and deepening of their study of the subject. It may be also useful for instructors running courses on functional analysis, supervising diploma theses or essays on various levels.

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