Linear Operators: General theory |
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Page 373
44] and for integrals by F. Riesz [2; p. 456]. Lemma 4.2 is due to F. Riesz [8; p. 36]
and was also used by Sz.-Nagy [5]. A similar argument may be applied to obtain
this result in any uniformly convex B-space. This generalizes and abstracts a ...
44] and for integrals by F. Riesz [2; p. 456]. Lemma 4.2 is due to F. Riesz [8; p. 36]
and was also used by Sz.-Nagy [5]. A similar argument may be applied to obtain
this result in any uniformly convex B-space. This generalizes and abstracts a ...
Page 388
1363] and F. Riesz [18]. Theorem. 7/1 < p < oo then a sequence {/„} converges
strongly to f in L„(S, E. n) if and only if it converges weakly and |/„| -> |/|. This
theorem remains valid in any uniformly convex R-space. Theorem 8.15 was
proved ...
1363] and F. Riesz [18]. Theorem. 7/1 < p < oo then a sequence {/„} converges
strongly to f in L„(S, E. n) if and only if it converges weakly and |/„| -> |/|. This
theorem remains valid in any uniformly convex R-space. Theorem 8.15 was
proved ...
Page 729
proofs, valid in uniformly convex spaces, were given by G. Birklioff [7] and F.
Riesz [16, 18]. Another proof, based on the interesting fact that a fixed point for a
contraction in Hilbert space is also a fixed point for its adjoint, was given by Riesz
...
proofs, valid in uniformly convex spaces, were given by G. Birklioff [7] and F.
Riesz [16, 18]. Another proof, based on the interesting fact that a fixed point for a
contraction in Hilbert space is also a fixed point for its adjoint, was given by Riesz
...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries 84 | 34 |
Copyright | |
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Common terms and phrases
Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero
Bibliographic information
| Title | Linear Operators: General theory Volume 7 of Pure and applied mathematics Volume 1 of Linear Operators, Nelson Dunford |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| Length | 2592 pages |
| Subjects | › › Algebra, Universal Algebras, Linear Linear operators Mathematical analysis Mathematics / Algebra / Linear |
| Export Citation | BiBTeX EndNote RefMan |