Linear Operators, Part 2 |
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Page 1971
... u . Since 0 = d ( \ 1 ( Ã1⁄2 ) ; Ãm ) → d ( u ; To ) , it follows that ... measurable function of I. The proof may be completed by choosing λ ( Ã ) to ... measurable map from S into B ( EP ) . Then there are E - measurable scalar ...
... u . Since 0 = d ( \ 1 ( Ã1⁄2 ) ; Ãm ) → d ( u ; To ) , it follows that ... measurable function of I. The proof may be completed by choosing λ ( Ã ) to ... measurable map from S into B ( EP ) . Then there are E - measurable scalar ...
Page 1989
... measure whose union differs from by a set of measure zero ... ( u ( o ) q ) ( s ) = p ( s ) , = 0 , SE σ , 8 € σ . It is clear that μ is a ... measurable and essentially bounded complex valued XV.11.3 1989 EXAMPLES OF BOUNDED SPECTRAL OPERATORS.
... measure whose union differs from by a set of measure zero ... ( u ( o ) q ) ( s ) = p ( s ) , = 0 , SE σ , 8 € σ . It is clear that μ is a ... measurable and essentially bounded complex valued XV.11.3 1989 EXAMPLES OF BOUNDED SPECTRAL OPERATORS.
Page 2082
... measure and let u be a positive measure defined on the Borel field Σ of a set S of complex numbers . Suppose that there exists a constant M such that | E ( 0 ) | ≤ Mμ ( o ) for all σ e Σ . Let x 。€ X and x * € X * , and let & be a ...
... measure and let u be a positive measure defined on the Borel field Σ of a set S of complex numbers . Suppose that there exists a constant M such that | E ( 0 ) | ≤ Mμ ( o ) for all σ e Σ . Let x 。€ X and x * € X * , and let & be a ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 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