Linear Operators, Part 1 |
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Page 263
Since G is an arbitrary open set containing F1-G, we have - Ali (F1) is Ž(G1)+-u1(
F1–G1). If F is a closed set it follows from this inequality, by allowing G1 to range
over all open sets containing FF, that u1(F1) is ul(FF1)+ug(F1–F). If E is an ...
Since G is an arbitrary open set containing F1-G, we have - Ali (F1) is Ž(G1)+-u1(
F1–G1). If F is a closed set it follows from this inequality, by allowing G1 to range
over all open sets containing FF, that u1(F1) is ul(FF1)+ug(F1–F). If E is an ...
Page 432
First, however, we prove the weaker assertion: if {ro * * * * > wo is an arbitrary
finite subset of 3:*, then there exists a ze A such that a **a* = a z, i = 1,..., n. To
see this, let m be an arbitrary integer; since a “* is in the 3'-closure of x(A), there is
an ...
First, however, we prove the weaker assertion: if {ro * * * * > wo is an arbitrary
finite subset of 3:*, then there exists a ze A such that a **a* = a z, i = 1,..., n. To
see this, let m be an arbitrary integer; since a “* is in the 3'-closure of x(A), there is
an ...
Page 476
N(T; A, e) = {RR e B(3, 9)), (T-R)r - e, a e A} where A is an arbitrary finite subset of
3., and e > 0 is arbitrary. Thus, in the strong topology, a generalized sequence {T.
} converges to T if and only if {T, who converges to Ta' for every a in 3.
N(T; A, e) = {RR e B(3, 9)), (T-R)r - e, a e A} where A is an arbitrary finite subset of
3., and e > 0 is arbitrary. Thus, in the strong topology, a generalized sequence {T.
} converges to T if and only if {T, who converges to Ta' for every a in 3.
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Contents
A Settheoretic Preliminaries | 1 |
Convergence and Uniform Convergence of Generalized | 26 |
Algebraic Preliminaries | 34 |
Copyright | |
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additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero
Bibliographic information
| Title | Linear Operators, Part 1 Linear Operators, Nelson Dunford Volume 1 of Linear Operators: General Theory. Spectral Theory, Self Adjoint Operators in Hilbert Space. Spectral Operators. I. II. III, Jacob T. Schwartz Volume 7 of Pure and applied mathematics : a series of texts and monographs Pure and applied mathematics, ISSN 0079-8185 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Edition | reprint |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |