Linear Operators: General theory |
From inside the book
Results 1-3 of 89
Page 106
Nelson Dunford, Jacob T. Schwartz. 10 Definition. The functions totally /x-
measurable on S, or, if fi is understood, totally measurable on S are the functions
in the closure TM(S) in F(S) of the /i-simple functions. If for every E in 27 with v(fi,
E) < oo ...
Nelson Dunford, Jacob T. Schwartz. 10 Definition. The functions totally /x-
measurable on S, or, if fi is understood, totally measurable on S are the functions
in the closure TM(S) in F(S) of the /i-simple functions. If for every E in 27 with v(fi,
E) < oo ...
Page 180
Since every real measurable function is the difference of two non- negative
measurable functions, it follows from the theorem that [•] j£ g(*Wd») = jEf(s)g(s)v(
ds), E € £, for a real measurable function g. Since the real and imaginary parts of
a ...
Since every real measurable function is the difference of two non- negative
measurable functions, it follows from the theorem that [•] j£ g(*Wd») = jEf(s)g(s)v(
ds), E € £, for a real measurable function g. Since the real and imaginary parts of
a ...
Page 663
Since the points in LP(S, E, fi) are not functions but classes of equivalent
functions, it is seen that T may not be ... Furthermore T is a continuous linear map
of the F-space M(S) = M(S, E, fi, X) of all X- valued fi-measurable functions into
itself.
Since the points in LP(S, E, fi) are not functions but classes of equivalent
functions, it is seen that T may not be ... Furthermore T is a continuous linear map
of the F-space M(S) = M(S, E, fi, X) of all X- valued fi-measurable functions into
itself.
What people are saying - Write a review
User Review - Flag as inappropriate
i want to read
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
79 other sections not shown
Other editions - View all
Common terms and phrases
a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact operator complex numbers complex valued contains continuous functions continuous linear convex set Corollary countably additive Definition denote dense differential equations disjoint sets Doklady Akad Duke Math element equivalent everywhere exists extended real valued extension finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality interval Lebesgue measure lim sup linear functional linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Riesz Russian semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space Trans uniformly unique v(fi valued function Vber vector valued weakly compact