Linear Operators: General theory |
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Page 761
... Proc . Nat . Acad . Sci . U.S.A. 32 , 156-161 ( 1946 ) . 9. Spectra and spectral manifolds . Ann . Soc . Polon ... Proc . Amer . Math . Soc . 5 , 589–595 ( 1954 ) . Halmos , P. R. , Lumer , G. , and Schäffer , J. J. 1. Square roots of ...
... Proc . Nat . Acad . Sci . U.S.A. 32 , 156-161 ( 1946 ) . 9. Spectra and spectral manifolds . Ann . Soc . Polon ... Proc . Amer . Math . Soc . 5 , 589–595 ( 1954 ) . Halmos , P. R. , Lumer , G. , and Schäffer , J. J. 1. Square roots of ...
Page 768
... Proc . Amer . Math . Soc . 3 , 874-883 ( 1952 ) . II . Izumi , S. 1 . 2 . 4 . On the bilinear functionals . Tôhoku Math . J. 42 , 195–209 ( 1936 ) . On the compactness of a class of functions . Proc . Imp . Acad . Tokyo 15 , 111-113 ...
... Proc . Amer . Math . Soc . 3 , 874-883 ( 1952 ) . II . Izumi , S. 1 . 2 . 4 . On the bilinear functionals . Tôhoku Math . J. 42 , 195–209 ( 1936 ) . On the compactness of a class of functions . Proc . Imp . Acad . Tokyo 15 , 111-113 ...
Page 821
... Proc . XII Scand . Math . Congress , Lund ( 1953 ) . 3. Commuting spectral measures on Hilbert space . Pacific J. Math . 4 , 355–361 ( 1954 ) . 4. On invariant subspaces of normal operators . Proc . Amer . Math . Soc . 3 , 270-277 ...
... Proc . XII Scand . Math . Congress , Lund ( 1953 ) . 3. Commuting spectral measures on Hilbert space . Pacific J. Math . 4 , 355–361 ( 1954 ) . 4. On invariant subspaces of normal operators . Proc . Amer . Math . Soc . 3 , 270-277 ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ