Linear Operators: General theory |
From inside the book
Results 1-3 of 12
Page 482
... commuting projections , E1 and E2 , will have the least upper bound and the greatest lower bound E1 v E2 = E1 + E2 - E1E2 , E1 ^ E2 = E1E2 . These two operations will be of fundamental importance in Volume II where we will introduce and ...
... commuting projections , E1 and E2 , will have the least upper bound and the greatest lower bound E1 v E2 = E1 + E2 - E1E2 , E1 ^ E2 = E1E2 . These two operations will be of fundamental importance in Volume II where we will introduce and ...
Page 592
... commuting with an operator S , and if f is a function analytic on a neighborhood of o ( S ) , then f is analytic on a neighborhood of o ( S + N ) , and f ( S + N ) = Σ n = 0 f ( n ) ( S ) Nn , n ! the series converging in the uniform ...
... commuting with an operator S , and if f is a function analytic on a neighborhood of o ( S ) , then f is analytic on a neighborhood of o ( S + N ) , and f ( S + N ) = Σ n = 0 f ( n ) ( S ) Nn , n ! the series converging in the uniform ...
Page 821
... Commuting spectral measures on Hilbert space . Pacific J. Math . 4 , 355–361 ( 1954 ) . 4 . 5 . 6 . 7 . 8 . On invariant subspaces of normal operators . Proc . Amer . Math . Soc . 3 , 270-277 ( 1952 ) . On restrictions of operators ...
... Commuting spectral measures on Hilbert space . Pacific J. Math . 4 , 355–361 ( 1954 ) . 4 . 5 . 6 . 7 . 8 . On invariant subspaces of normal operators . Proc . Amer . Math . Soc . 3 , 270-277 ( 1952 ) . On restrictions of operators ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
80 other sections not shown
Other editions - View all
Common terms and phrases
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