Linear Operators: General theory |
From inside the book
Results 1-3 of 49
Page 475
... topology and the weak , or X * , topology . If X is the conjugate space of Y , there is also the topology in X. The ... operator topologies , as given in the following definitions . 1 DEFINITION . The uniform operator topology in B ( X ...
... topology and the weak , or X * , topology . If X is the conjugate space of Y , there is also the topology in X. The ... operator topologies , as given in the following definitions . 1 DEFINITION . The uniform operator topology in B ( X ...
Page 512
... operator topology . Conversely , if the closed unit . sphere of B ( X , Y ) is compact in the weak operator topology , Y is reflexive . 7 Define the BWO topology for B ( X , Y ) to be the strongest topology which coincides with the weak ...
... operator topology . Conversely , if the closed unit . sphere of B ( X , Y ) is compact in the weak operator topology , Y is reflexive . 7 Define the BWO topology for B ( X , Y ) to be the strongest topology which coincides with the weak ...
Page 593
... operator topology and later discuss the same question when B ( X ) has the weak or the strong operator topologies . Note that if f ( 2 ) ‡ 0 for λ e σ ( T ) , then ƒ ( T ) has a bounded in- verse , and hence ƒ „ ( T ) = [ ƒ ( T ) ] - 1ƒ ...
... operator topology and later discuss the same question when B ( X ) has the weak or the strong operator topologies . Note that if f ( 2 ) ‡ 0 for λ e σ ( T ) , then ƒ ( T ) has a bounded in- verse , and hence ƒ „ ( T ) = [ ƒ ( T ) ] - 1ƒ ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ