Linear Operators: General theory |
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Page 37
If T : X -»□ 7) and U : 3) -*□ 3 are linear transformations, and X, 'J), 3 are linear
spaces over the same field 0, the product UT, defined by (UT)x = U(Tx), is a linear
transformation which maps X into 3- If T is a linear operator on X to X, it is said to
...
If T : X -»□ 7) and U : 3) -*□ 3 are linear transformations, and X, 'J), 3 are linear
spaces over the same field 0, the product UT, defined by (UT)x = U(Tx), is a linear
transformation which maps X into 3- If T is a linear operator on X to X, it is said to
...
Page 486
The set of compact operators is closed in the uniform operator topology of ). ...
Linear combinations of compact linear operators are compact operators, and any
product of a compact linear operator and a hounded linear operator is a compact
...
The set of compact operators is closed in the uniform operator topology of ). ...
Linear combinations of compact linear operators are compact operators, and any
product of a compact linear operator and a hounded linear operator is a compact
...
Page 494
Conversely, let /j, be an X-valued measure defined on the Borel sets in £ with the
property that x*u is in rca(S) for every x* in X*. It is clear that the operator T,
defined by (b), is a bounded linear operator on C(S) to X whose adjoint T* is
given by ...
Conversely, let /j, be an X-valued measure defined on the Borel sets in £ with the
property that x*u is in rca(S) for every x* in X*. It is clear that the operator T,
defined by (b), is a bounded linear operator on C(S) to X whose adjoint T* is
given by ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries 84 | 34 |
Copyright | |
44 other sections not shown
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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
Bibliographic information
| Title | Linear Operators: General theory Volume 7 of Pure and applied mathematics Volume 1 of Linear Operators, Nelson Dunford |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| Length | 2592 pages |
| Subjects | › › Algebra, Universal Algebras, Linear Linear operators Mathematical analysis Mathematics / Algebra / Linear |
| Export Citation | BiBTeX EndNote RefMan |