Linear Operators: General theory |
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Page 45
... matrix ( a ;; ) . If T is a linear operator , then it can be shown that the determinants of the matrices of T in terms of any two bases are equal , and so we may and shall call their common value the determinant of T , denoted by det ...
... matrix ( a ;; ) . If T is a linear operator , then it can be shown that the determinants of the matrices of T in terms of any two bases are equal , and so we may and shall call their common value the determinant of T , denoted by det ...
Page 75
... matrix ( a ,, ) is said to define a regular method of summability . 36 ( Silverman - Toeplitz ) . Show that a matrix ( a ,, ) defines a regular method of summability if and only if ( a ) lub Σ = 1 1 < i < ∞ | as | - M < ∞ ; ( b ) lim ...
... matrix ( a ,, ) is said to define a regular method of summability . 36 ( Silverman - Toeplitz ) . Show that a matrix ( a ,, ) defines a regular method of summability if and only if ( a ) lub Σ = 1 1 < i < ∞ | as | - M < ∞ ; ( b ) lim ...
Page 607
... matrix were used almost from the beginning of the theory , and by 1867 Laguerre [ 1 ] had considered infinite power series in a matrix in constructing the exponential function of a matrix . Sylvester [ 1 , 2 ] constructed arbitrary ...
... matrix were used almost from the beginning of the theory , and by 1867 Laguerre [ 1 ] had considered infinite power series in a matrix in constructing the exponential function of a matrix . Sylvester [ 1 , 2 ] constructed arbitrary ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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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