Linear Operators: General theory |
From inside the book
Results 1-3 of 92
Page 20
A sequence { an } is said to be convergent if an → a for some a . A sequence { an
} in a metric space is a Cauchy sequence if limm . n olan , an ) = 0 . If every
Cauchy sequence is convergent , a metric space is said to be complete . The next
...
A sequence { an } is said to be convergent if an → a for some a . A sequence { an
} in a metric space is a Cauchy sequence if limm . n olan , an ) = 0 . If every
Cauchy sequence is convergent , a metric space is said to be complete . The next
...
Page 68
The space X is said to be weakly complete if every weak Cauchy sequence has a
weak limit . In Chapter V , a topology is introduced in certain linear spaces in
such a way that they become Hausdorff spaces in which the notion of
convergence ...
The space X is said to be weakly complete if every weak Cauchy sequence has a
weak limit . In Chapter V , a topology is introduced in certain linear spaces in
such a way that they become Hausdorff spaces in which the notion of
convergence ...
Page 345
Show that a sequence of functions in A ( D ) is a weak Cauchy sequence ( a
sequence converging weakly to f in A ( D ) ) if and only if it is uniformly bounded
and converges at each point of the boundary of D ( to f ) . Show that a subset of A
...
Show that a sequence of functions in A ( D ) is a weak Cauchy sequence ( a
sequence converging weakly to f in A ( D ) ) if and only if it is uniformly bounded
and converges at each point of the boundary of D ( to f ) . Show that a subset of A
...
What people are saying - Write a review
User Review - Flag as inappropriate
i want to read
Contents
Metric Spaces | 19 |
Convergence and Uniform Convergence of Generalized | 26 |
Exercises | 33 |
Copyright | |
10 other sections not shown
Other editions - View all
Common terms and phrases
Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero
References to this book
Bibliographic information
| Title | Linear Operators: General theory Part 1 of Linear Operators, Jacob T. Schwartz Volume 1; Volume 7 of Pure and applied mathematics : a series of texts and monographs Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics, ISSN 0079-8185 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| ISBN | 0470226056, 9780470226056 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |