Linear Operators: Spectral operators |
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Page 60
... uniformly bounded if there exists a fixed polynomial p(k) such that for all adversaries A, there is a negligible function ε A, such that for all k ≥ 0, Pr [ XA(k) > p(k) ] ≤ ε A(k). A protocol statistic X is called probabilistically ...
... uniformly bounded if there exists a fixed polynomial p(k) such that for all adversaries A, there is a negligible function ε A, such that for all k ≥ 0, Pr [ XA(k) > p(k) ] ≤ ε A(k). A protocol statistic X is called probabilistically ...
Page 138
... uniformly bounded . For example , let 1 n't , if 0≤ts xn ( t ) n = 1 1 if < t < 1 n for n = 1 , 2 , .... Then x ( t ) = C ( [ 0 , 1 ] ) , în ( 0 ) = 0 and x ( t ) | ≤ 1 ... Bounded Linear Maps on Banach Spaces Uniform Boundedness Principle.
... uniformly bounded . For example , let 1 n't , if 0≤ts xn ( t ) n = 1 1 if < t < 1 n for n = 1 , 2 , .... Then x ( t ) = C ( [ 0 , 1 ] ) , în ( 0 ) = 0 and x ( t ) | ≤ 1 ... Bounded Linear Maps on Banach Spaces Uniform Boundedness Principle.
Page 246
... bounded . This means that for each x Є R there exists a number Mx ≥ 0 such that | ƒ ( x ) | ≤ Mx for all ƒ Є F. We can describe this situation by saying that F is pointwise bounded . Does this imply that the collection is uniformly ...
... bounded . This means that for each x Є R there exists a number Mx ≥ 0 such that | ƒ ( x ) | ≤ Mx for all ƒ Є F. We can describe this situation by saying that F is pointwise bounded . Does this imply that the collection is uniformly ...
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