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 2091
... convex spaces . The generalization , however , is not done in a routine fashion but is substantially recast . Let E be a locally convex linear Hausdorff space which is " quasi - complete and barreled . ” Ionescu Tulcea [ 3 ] introduces ...
... convex spaces . The generalization , however , is not done in a routine fashion but is substantially recast . Let E be a locally convex linear Hausdorff space which is " quasi - complete and barreled . ” Ionescu Tulcea [ 3 ] introduces ...
Page 2109
... convex spaces . For instance : ( a ) Let fe D ( T " ) be a distribution on the n - dimensional torus T " ; then the convolution mappings u → fu on the spaces Co ( T " ) or D ( T ) are scalar . Thus differential operators with constant ...
... convex spaces . For instance : ( a ) Let fe D ( T " ) be a distribution on the n - dimensional torus T " ; then the convolution mappings u → fu on the spaces Co ( T " ) or D ( T ) are scalar . Thus differential operators with constant ...
Page 2551
... convex spaces . Dissertation , Yale Univ . , 1961 . 2 . 3 . A characterization of spectral operators on locally convex spaces . Math . Ann . 143 , 59-74 ( 1961 ) . Remarks on spectra of operators on a locally convex space . Proc . Nat ...
... convex spaces . Dissertation , Yale Univ . , 1961 . 2 . 3 . A characterization of spectral operators on locally convex spaces . Math . Ann . 143 , 59-74 ( 1961 ) . Remarks on spectra of operators on a locally convex space . Proc . Nat ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra 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 denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem 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