Linear Operators, Part 2 |
From inside the book
Results 1-3 of 90
Page 2084
... complex B - space X which satisfies the growth condition ( * ) in Theorem XV.6.7 , namely K ( * ) | R ( § ; T. ) E ( 0 ) | ≤ dist ( § , ō ) m for έ & ō , | § | ≤ | T | + 1. If k is a natural number then there exists a constant M such ...
... complex B - space X which satisfies the growth condition ( * ) in Theorem XV.6.7 , namely K ( * ) | R ( § ; T. ) E ( 0 ) | ≤ dist ( § , ō ) m for έ & ō , | § | ≤ | T | + 1. If k is a natural number then there exists a constant M such ...
Page 2171
... complex B - space X. For each x in x the symbol [ x ] will be used for the closed linear manifold determined by all the vectors R ( § ; T ) x with έ in p ( T ) . If σ is a closed set of complex numbers , the symbol M ( o ) will denote ...
... complex B - space X. For each x in x the symbol [ x ] will be used for the closed linear manifold determined by all the vectors R ( § ; T ) x with έ in p ( T ) . If σ is a closed set of complex numbers , the symbol M ( o ) will denote ...
Page 2188
... complex B - space X which is defined and countably additive on a o - field Σ of subsets of a set A and let g be a bounded Borel measurable function defined on the complex plane . Then √ g ( f ( x ) ) E ( dx ) = √ , 9 ( μ ) E ( ƒ − 1 ...
... complex B - space X which is defined and countably additive on a o - field Σ of subsets of a set A and let g be a bounded Borel measurable function defined on the complex plane . Then √ g ( f ( x ) ) E ( dx ) = √ , 9 ( μ ) E ( ƒ − 1 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
26 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero