Linear Operators: General theory |
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Page 611
... adjoint operator T in L2 ( — ∞ , ∞ ) has a countable set of isolated eigenvalues of finite multiplicity with 2 = 0 as the only limit point of o ( T ) , then T is unitarily equivalent to an integral operator of a certain classical ...
... adjoint operator T in L2 ( — ∞ , ∞ ) has a countable set of isolated eigenvalues of finite multiplicity with 2 = 0 as the only limit point of o ( T ) , then T is unitarily equivalent to an integral operator of a certain classical ...
Page 612
... adjoint operator ( which may have void point spectrum ) on a separable Hilbert space , then a self adjoint compact operator K may be found such that T + K has enough eigenvectors to span the entire space . This result was extended to ...
... adjoint operator ( which may have void point spectrum ) on a separable Hilbert space , then a self adjoint compact operator K may be found such that T + K has enough eigenvectors to span the entire space . This result was extended to ...
Page 794
... operator . Izvestiya Akad . Nauk SSSR 4 , 53–104 ( 1940 ) . ( Russian ... adjoint differential operators of the second order . Doklady Akad . Nauk ... adjoint differential operators of the second order . Uspehi Matem . Nauk ( N. S. ) 8 ...
... operator . Izvestiya Akad . Nauk SSSR 4 , 53–104 ( 1940 ) . ( Russian ... adjoint differential operators of the second order . Doklady Akad . Nauk ... adjoint differential operators of the second order . Uspehi Matem . Nauk ( N. S. ) 8 ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ