Linear Operators: General theory |
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Page 243
... unitary space En is a Hilbert space , if the inner product ( x , y ) of two elements x = [ 1 , ... ,, ] and y = [ ẞ1 , ... , ẞn ] in En is defined by the formula In the same way , complex n ( x , y ) = Σαβι . i = 1 l is a Hilbert space ...
... unitary space En is a Hilbert space , if the inner product ( x , y ) of two elements x = [ 1 , ... ,, ] and y = [ ẞ1 , ... , ẞn ] in En is defined by the formula In the same way , complex n ( x , y ) = Σαβι . i = 1 l is a Hilbert space ...
Page 555
... unitary space leads to a rather complete description of the analytic behavior of the operator and , at the same time , furnishes a clear geometric picture of the manner in which the operator transforms the unitary space upon which it ...
... unitary space leads to a rather complete description of the analytic behavior of the operator and , at the same time , furnishes a clear geometric picture of the manner in which the operator transforms the unitary space upon which it ...
Page 728
... unitary operators in L ( S ) . Von Neumann's proof was based on the spectral theory of unitary operators in Hilbert space . Many exten- sions and generalizations of this ergodic theorem have been given , both to more general B - spaces ...
... unitary operators in L ( S ) . Von Neumann's proof was based on the spectral theory of unitary operators in Hilbert space . Many exten- sions and generalizations of this ergodic theorem have been given , both to more general B - spaces ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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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