Linear Operators: General theory |
From inside the book
Results 1-3 of 38
Page 311
Consider the closed subspace B(S, E) of B(S). According to Theorems 6.18 and
6.20 there is a compact Hausdorff space St such that B(S, E) is equivalent to C(
5X). Theorem 5.1 shows that there is an isometric isomorphism x* •< — * fi
between ...
Consider the closed subspace B(S, E) of B(S). According to Theorems 6.18 and
6.20 there is a compact Hausdorff space St such that B(S, E) is equivalent to C(
5X). Theorem 5.1 shows that there is an isometric isomorphism x* •< — * fi
between ...
Page 313
The correspondence U : fa -> fa is an isometric isomorphism of ba(Sv EJ onto ca(
Sv E2). (c) // E1 is in Ex tfien v{fa, Et) = v(U(fa), Er) for all fa in ba(SvEl). Proof.
Recalling that t is an isomorphism of E onto Ev it is clear that the mapping T is an
...
The correspondence U : fa -> fa is an isometric isomorphism of ba(Sv EJ onto ca(
Sv E2). (c) // E1 is in Ex tfien v{fa, Et) = v(U(fa), Er) for all fa in ba(SvEl). Proof.
Recalling that t is an isomorphism of E onto Ev it is clear that the mapping T is an
...
Page 337
Thus, ba(S, E) is isometrically isomorphic with the closed subspace BV0(I) of all /
e BV(I) such that/(a + ) = 0. If N is the ... Thus / •« — *□ fif determines an isometric
isomorphism between NBV(I) and rba(I, E). Using Theorem 9.9, we obtain the ...
Thus, ba(S, E) is isometrically isomorphic with the closed subspace BV0(I) of all /
e BV(I) such that/(a + ) = 0. If N is the ... Thus / •« — *□ fif determines an isometric
isomorphism between NBV(I) and rba(I, E). Using Theorem 9.9, we obtain the ...
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 84 | 34 |
Copyright | |
44 other sections not shown
Other editions - View all
Common terms and phrases
Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma 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 properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero