Some Results on Grothendieck's Condition f double prime for the Approximability of Compact Operators.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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In this work the author presents a new approach to the problem of approximability of compact linear operators, starting from a form of this problem given by Grothendieck in terms of infinite matrices. This form says that, for matrices P in a certain class, the condition P sup 2 0 implies trace of P 0. The author uses this condition more specifically and resort less to more refined properties of determinants than does Grothendieck. In particular the author is able to enlarge a subclass given by Grothendieck for which the above property on the trace holds and the author formulates new assumptions for its validity in the general case. Author
- Theoretical Mathematics