Linear Operators, Part 2 |
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Page 1061
Thus | 1199 = sup SH1 ( x ) g ( x ) dx = Kyl / lp , = by Theorem IV.8.1 , the Hahn - Banach theorem ( II.3.14 ) and Hölder's inequality , and the theorem is proved for all p , 1 < p < 0. Q.E.D. Having proved the basic inequality of M.
Thus | 1199 = sup SH1 ( x ) g ( x ) dx = Kyl / lp , = by Theorem IV.8.1 , the Hahn - Banach theorem ( II.3.14 ) and Hölder's inequality , and the theorem is proved for all p , 1 < p < 0. Q.E.D. Having proved the basic inequality of M.
Page 1105
We now pause to sharpen another of the inequalities of Lemma 9 . ... the continuity of the norm function which follows from the triangle inequality of Lemma 14 ( d ) , and by Lemma 11 , it follows that we may without loss of generality ...
We now pause to sharpen another of the inequalities of Lemma 9 . ... the continuity of the norm function which follows from the triangle inequality of Lemma 14 ( d ) , and by Lemma 11 , it follows that we may without loss of generality ...
Page 1774
The above inequality , known as the Schwarz inequality , will be proved first . It follows from the postulates for H that the Schwarz inequality is valid if either x or y is zero . Hence suppose that x # 0 #y . For an arbitrary complex ...
The above inequality , known as the Schwarz inequality , will be proved first . It follows from the postulates for H that the Schwarz inequality is valid if either x or y is zero . Hence suppose that x # 0 #y . For an arbitrary complex ...
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Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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