Linear Operators: General theory |
From inside the book
Results 1-3 of 72
Page 256
... Hilbert spaces then it will always be understood , sometimes without explicit mention , that X is the uniquely deter- mined Hilbert space with scalar product ( iv ) ( [ x1 , . . . , xn ] , [ Y1 , • • • , Yn ] ) = n Σ ( xi , Yi ) i i = 1 ...
... Hilbert spaces then it will always be understood , sometimes without explicit mention , that X is the uniquely deter- mined Hilbert space with scalar product ( iv ) ( [ x1 , . . . , xn ] , [ Y1 , • • • , Yn ] ) = n Σ ( xi , Yi ) i i = 1 ...
Page 479
... Hilbert space adjoint of T. Let us give a formal definition . 9 DEFINITION . Let be a Hilbert space , and let T € B ( § ) . There is a uniquely determined operator T * € B ( ) , called the Hilbert space adjoint of T , which satisfies ...
... Hilbert space adjoint of T. Let us give a formal definition . 9 DEFINITION . Let be a Hilbert space , and let T € B ( § ) . There is a uniquely determined operator T * € B ( ) , called the Hilbert space adjoint of T , which satisfies ...
Page 480
... Hilbert space , will refer to the Hilbert space adjoint . An operator T in Hilbert space is called self- adjoint if T * = T. The preceding lemmas concerning adjoints take the following form in Hilbert space . 10 LEMMA . If T and U are ...
... Hilbert space , will refer to the Hilbert space adjoint . An operator T in Hilbert space is called self- adjoint if T * = T. The preceding lemmas concerning adjoints take the following form in Hilbert space . 10 LEMMA . If T and U are ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
59 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 Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism 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 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ