Linear Operators: Spectral operators |
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Page 2256
... subset σ of o ( T ) which is open in the relative . topology of o ( T ) . It follows that the set 7 ( σ ) = { z | z ̄1 e σ } is a compact subset of o ( R ) , open in the relative topology of o ( R ) . Thus each point in o ( R ) ...
... subset σ of o ( T ) which is open in the relative . topology of o ( T ) . It follows that the set 7 ( σ ) = { z | z ̄1 e σ } is a compact subset of o ( R ) , open in the relative topology of o ( R ) . Thus each point in o ( R ) ...
Page 2257
... subsets of o ( R ) which do not contain 0. Since by assumption E ( o ; T ) | is uniformly bounded for o in K , since each compact open subset 01 of o ( R ) is either a compact open subset of o ( R ) not con- taining zero or the ...
... subsets of o ( R ) which do not contain 0. Since by assumption E ( o ; T ) | is uniformly bounded for o in K , since each compact open subset 01 of o ( R ) is either a compact open subset of o ( R ) not con- taining zero or the ...
Page 2309
... subset of the complex plane . Let R1 be a subset of the complex plane , and ƒ a function defined in RX R1 . Let { g } be a sequence of functions defined in the set R1 . Suppose that , for each N , N lim | 2 | " | ƒ ( z , w ) – Σ In ( w ) ...
... subset of the complex plane . Let R1 be a subset of the complex plane , and ƒ a function defined in RX R1 . Let { g } be a sequence of functions defined in the set R1 . Suppose that , for each N , N lim | 2 | " | ƒ ( z , w ) – Σ In ( w ) ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero