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By Robert Schatten

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Extra resources for A theory of cross-spaces

Sample text

It. equivalent to = Tf/C and . equivalent to is also where Pf . the closed linear T^

LEMMA /^ implies Proof. 2. 2. ^0 0^ consequence T^7^ . Then, . 2. Crossnorms. Among the norms oC on "crossnorms", that is, norms ^ ^^ of particular interest are the satisfying the following additional condition: 28 CROSSNORMS II. V. <*( Therefore, a = g) norm is a f I/ II g I/ IJ crossnorm and only if which generate operators from 1^ into if, its value for the expressions ^ l^of rank equal to the bound is 1 of the generated operators. At this point make use it seems proper of in the future: given crossnorm ot , detail in the following LEMMA of the ?

1. Tg. - the "inner product* sents an additive functional on Since by definition f^j ^v 1j is O^^ dense in Theorem (2^, fecting the value of its bound. 2. V p. 180J explained above. , We may with a bound equal to O(^ "^^otTra^ ,this functional T^

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A theory of cross-spaces by Robert Schatten

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