Linear Operators, Part 2 |
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Page 2108
... exists a partial order of A for which both μ and v are positive . This result throws light on when the sum and ... exists a compact space X , a spectral measure μ on X to A and a bounded Baire measurable function f : XC such that a Sf ...
... exists a partial order of A for which both μ and v are positive . This result throws light on when the sum and ... exists a compact space X , a spectral measure μ on X to A and a bounded Baire measurable function f : XC such that a Sf ...
Page 2405
... exists for μ - almost all s , and that , writing If , for the norm of an element f of L , ( S , E , μ ) , we have | Ãh | , ≤ { A } , \ h \ , . Thus , using Theorem III.2.22 ( a ) , we see that if 2 ≤r < ∞ , and if g is any complex ...
... exists for μ - almost all s , and that , writing If , for the norm of an element f of L , ( S , E , μ ) , we have | Ãh | , ≤ { A } , \ h \ , . Thus , using Theorem III.2.22 ( a ) , we see that if 2 ≤r < ∞ , and if g is any complex ...
Page 2418
... exists for almost all z " e D. Therefore , by Tonelli's theorem ( III.11.14 ) , the integral ( 75 ) SS 141 ( 2 " , 2 ) | | A2 ( z , z ' ) | If ( z ' ) dx ' dy ' dx dy - D D exists for almost all z " e D. It follows from ( 65 ) and ( 68 ) ...
... exists for almost all z " e D. Therefore , by Tonelli's theorem ( III.11.14 ) , the integral ( 75 ) SS 141 ( 2 " , 2 ) | | A2 ( z , z ' ) | If ( z ' ) dx ' dy ' dx dy - D D exists for almost all z " e D. It follows from ( 65 ) and ( 68 ) ...
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