Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
From inside the book
Results 1-3 of 86
Page 1990
... vector valued function , or a principal value integral of a vector valued function . For a given in 5 and a point t in RN the translate p , in H , defined as H Фе Pt ( s ) = q ( st ) , when regarded as a map t → of RN into H , is ...
... vector valued function , or a principal value integral of a vector valued function . For a given in 5 and a point t in RN the translate p , in H , defined as H Фе Pt ( s ) = q ( st ) , when regarded as a map t → of RN into H , is ...
Page 2074
... vector x in 5 , is uniquely determined by y . In other words , the operator a is one - to - one on H + . Now let y be an arbitrary vector in H + and define the vector x by the equation ( 36 ) . Then ( 31 ) shows that x is in H + and ...
... vector x in 5 , is uniquely determined by y . In other words , the operator a is one - to - one on H + . Now let y be an arbitrary vector in H + and define the vector x by the equation ( 36 ) . Then ( 31 ) shows that x is in H + and ...
Page 2266
... vector x is sp { Ex | E ɛ B } . A projection E e B will be said to satisfy the countable chain condition if every family of disjoint projections in B bounded by E is at most countable . We shall denote by the set of all Ee B satisfying ...
... vector x is sp { Ex | E ɛ B } . A projection E e B will be said to satisfy the countable chain condition if every family of disjoint projections in B bounded by E is at most countable . We shall denote by the set of all Ee B satisfying ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero