Linear Operators: General theory |
From inside the book
Results 1-3 of 73
Page 169
5 Show that (i), (ii), and (iii) of Theorem 8.6 imply that / is in LV(S, Z, fi) and that |/„
— /|„ converges to zero even if {/„} is a generalized sequence. 6 Let fi be bounded
. Suppose that the field Z is separable under the metric q(E, F) = v(/j,, EA F).
5 Show that (i), (ii), and (iii) of Theorem 8.6 imply that / is in LV(S, Z, fi) and that |/„
— /|„ converges to zero even if {/„} is a generalized sequence. 6 Let fi be bounded
. Suppose that the field Z is separable under the metric q(E, F) = v(/j,, EA F).
Page 204
Since fi(Fn) = Js^/n^K^^) does not converge to zero and since 0 fn(sai) ^ 1 it
follows from the dominated convergence theorem (6.16) that there is a point in for
which /„(s2,) 's defined for all n and for which the sequence )} does not converge
to ...
Since fi(Fn) = Js^/n^K^^) does not converge to zero and since 0 fn(sai) ^ 1 it
follows from the dominated convergence theorem (6.16) that there is a point in for
which /„(s2,) 's defined for all n and for which the sequence )} does not converge
to ...
Page 452
If A is a subset of X, and p is in A, then there exists a non-zero continuous linear
functional tangent to A at p if and only if the cone B with vertex p generated by A
is not dense in X. Proof. If q 4 K, then, by 2.12 we can find a functional / and a real
...
If A is a subset of X, and p is in A, then there exists a non-zero continuous linear
functional tangent to A at p if and only if the cone B with vertex p generated by A
is not dense in X. Proof. If q 4 K, then, by 2.12 we can find a functional / and a real
...
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 | |
78 other sections not shown
Other editions - View all
Common terms and phrases
additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations disjoint Doklady Akad Duke Math element ergodic theorem exists finite dimensional function defined Hausdorff space Hence Hilbert space homeomorphism ibid inequality integral Lebesgue Lebesgue measure Lemma linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc Proof properties proved real numbers reflexive Riesz Russian Sbornik N. S. scalar self-adjoint semi-group sequentially compact Show simple functions spectral Studia Math subset subspace Suppose theory topological space Trans uniformly Univ valued function Vber vector space weak topology weakly compact zero
Bibliographic information
| Title | Linear Operators: General theory Volume 7 of Pure and applied mathematics Volume 1 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics Interscience Press |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 16 Mar 2011 |
| Length | 2592 pages |
| Subjects | › › Algebra, Universal Algebras, Linear Linear operators Mathematical analysis Mathematics / Algebra / Linear Mathematics / Mathematical Analysis |
| Export Citation | BiBTeX EndNote RefMan |