Linear Operators: General theory |
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Page 46
... C ( i , ... , ipi 11 . jp ) , then the Laplace expansion of det ( a ) in terms of the elements of the i , ... , ith rows is given by the formula ... , ip ) × C ( i1 , . . . , ip ; Î19 · · · , İp ) , . . .... ipi i det ( as ) Σ B ( i ...
... C ( i , ... , ipi 11 . jp ) , then the Laplace expansion of det ( a ) in terms of the elements of the i , ... , ith rows is given by the formula ... , ip ) × C ( i1 , . . . , ip ; Î19 · · · , İp ) , . . .... ipi i det ( as ) Σ B ( i ...
Page 344
... C ( I ) determines an isometric isomorphism between C ( I ) * and NBV ( I ) . Show that if { g } is a sequence of functions in NBV ( I ) , we have lim , → ∞ Sif ( s ) dgn ( s ) = Sif ( s ) dgo ( s ) for all fin C ( I ) if and only if ...
... C ( I ) determines an isometric isomorphism between C ( I ) * and NBV ( I ) . Show that if { g } is a sequence of functions in NBV ( I ) , we have lim , → ∞ Sif ( s ) dgn ( s ) = Sif ( s ) dgo ( s ) for all fin C ( I ) if and only if ...
Page 558
... ( c ) I = E ( 2 ) . Σ λεσ ( Τ ) Let { 21 , ... , 2 } be an enumeration of o ( T ) , and let X , X ; It follows from ( b ) and ( c ) of Theorem 6 that X = 1 X1 ... X. = E ( 1 ) X . Moreover , since TE ( 2 , ) = E ( 2 , ) T , it follows ...
... ( c ) I = E ( 2 ) . Σ λεσ ( Τ ) Let { 21 , ... , 2 } be an enumeration of o ( T ) , and let X , X ; It follows from ( b ) and ( c ) of Theorem 6 that X = 1 X1 ... X. = E ( 1 ) X . Moreover , since TE ( 2 , ) = E ( 2 , ) T , it follows ...
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