Linear Operators, Part 1 |
From inside the book
Results 1-3 of 91
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 , glam , an ) = 0. If every Cauchy
sequence is convergent , a metric space is said to be complete . The next three ...
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 , glam , an ) = 0. If every Cauchy
sequence is convergent , a metric space is said to be complete . The next three ...
Page 68
which converges weakly to a point in X. Every sequence { xn } such that { x * xn }
is a Cauchy sequence of scalars for each x * e X * is called a weak Cauchy
sequence . The space X is said to be weakly complete if every weak Cauchy ...
which converges weakly to a point in X. Every sequence { xn } such that { x * xn }
is a Cauchy sequence of scalars for each x * e X * is called a weak Cauchy
sequence . The space X is said to be weakly complete if every weak Cauchy ...
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
( D ) ...
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
( D ) ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
87 other sections not shown
Other editions - View all
Common terms and phrases
Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators, Part 1 Linear Operators, Jacob T. Schwartz Volume 7 of Mathematics, Pure, Applied Volume 7 of Pure and applied mathematics, ISSN 0079-8185 Volume 7 of Pure and applied mathematics. A series of texts and monographs |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |