Linear Operators: General theory |
From inside the book
Results 1-3 of 81
Page 373
This generalizes and abstracts a result proved for closed linear manifolds in L2 [
0 , 1 ] by E . Fischer ( 2 ] . The fact that a linear manifold which is not dense in the
entire space has a non - zero orthogonal complement ( proved in 4 . 4 ) was ...
This generalizes and abstracts a result proved for closed linear manifolds in L2 [
0 , 1 ] by E . Fischer ( 2 ] . The fact that a linear manifold which is not dense in the
entire space has a non - zero orthogonal complement ( proved in 4 . 4 ) was ...
Page 385
27 . They are essentially due , at least in the real case , to Stone [ 1 ] , although
his terminology and proofs often differ from that given here . It should be
mentioned that Theorem 6 . 22 was proved independently by Cech [ 1 ] only
slightly later .
27 . They are essentially due , at least in the real case , to Stone [ 1 ] , although
his terminology and proofs often differ from that given here . It should be
mentioned that Theorem 6 . 22 was proved independently by Cech [ 1 ] only
slightly later .
Page 608
In the case of a bounded or unbounded normal operator in a Hilbert space ,
many of the results of this section become simpler and can be proved more
directly by other methods . With these hypotheses considerable extension is
possible .
In the case of a bounded or unbounded normal operator in a Hilbert space ,
many of the results of this section become simpler and can be proved more
directly by other methods . With these hypotheses considerable extension is
possible .
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 |