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 |
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Page 1945
... Hilbert Space What is the relationship between the bounded spectral operators in a Hilbert space H and the bounded normal operators in ? The central result in this direction is a theorem of Wermer which states that every scalar type ...
... Hilbert Space What is the relationship between the bounded spectral operators in a Hilbert space H and the bounded normal operators in ? The central result in this direction is a theorem of Wermer which states that every scalar type ...
Page 2169
... Hilbert Space It is the purpose of this section to show how the theory of spectral operators may be applied to yield the classical spectral theorem in Hilbert space , that is , the theorem asserting that a bounded self adjoint operator in ...
... Hilbert Space It is the purpose of this section to show how the theory of spectral operators may be applied to yield the classical spectral theorem in Hilbert space , that is , the theorem asserting that a bounded self adjoint operator in ...
Page 2528
... Hilbert space . Pacific J. Math . 13 , 551-562 ( 1963 ) . 10. A counterexample to a problem of Sz . - Nagy . Proc . Amer . Math . Soc . 15 , 788- 790 ( 1964 ) . 11 . Weak limits of powers of a contraction in Hilbert space . Proc . Amer ...
... Hilbert space . Pacific J. Math . 13 , 551-562 ( 1963 ) . 10. A counterexample to a problem of Sz . - Nagy . Proc . Amer . Math . Soc . 15 , 788- 790 ( 1964 ) . 11 . Weak limits of powers of a contraction in Hilbert space . Proc . Amer ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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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