Linear Operators: General theory |
From inside the book
Results 1-3 of 70
Page 136
6 LEMMA . There is a uniquely determined smallest field and a uniquely
determined smallest o - field containing a given family of sets . PROOF . There is
at least one field , namely the field of all subsets of S , which contains a given
family t .
6 LEMMA . There is a uniquely determined smallest field and a uniquely
determined smallest o - field containing a given family of sets . PROOF . There is
at least one field , namely the field of all subsets of S , which contains a given
family t .
Page 454
... to - one mapping of K is a homeomorphism , ( cf . Lemma I . 5 . 8 ) , changing to
the X * topology does not affect the hypotheses of the lemma . We will say that a
set of continuous linear functionals F = { f } is determined by another set G = { g } ...
... to - one mapping of K is a homeomorphism , ( cf . Lemma I . 5 . 8 ) , changing to
the X * topology does not affect the hypotheses of the lemma . We will say that a
set of continuous linear functionals F = { f } is determined by another set G = { g } ...
Page 455
Let G = U _ Yn ; then f is determined by G . It follows that if F is a denumerable
subset of X * , there exists a denumerable subset G , of X * such that each je F is
determined by GF . We can even assert that each continuous linear functional |
can ...
Let G = U _ Yn ; then f is determined by G . It follows that if F is a denumerable
subset of X * , there exists a denumerable subset G , of X * such that each je F is
determined by GF . We can even assert that each continuous linear functional |
can ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators: General theory Volume 1 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics |
| Author | Nelson Dunford |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 16 Mar 2011 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |