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Operators of Rademacher and Gaussian Subcotype
Author(s) -
Hinrichs Aicke
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1017/s0024610700001861
Subject(s) - banach space , mathematics , bounded function , sequence (biology) , norm (philosophy) , operator norm , linear operators , class (philosophy) , bounded operator , discrete mathematics , operator (biology) , combinatorics , gaussian , operator theory , mathematical analysis , computer science , physics , repressor , artificial intelligence , law , chemistry , genetics , biology , biochemistry , political science , transcription factor , gene , quantum mechanics
For a linear and bounded operator T from a Banach space X into a Banach space Y , let ϱ( T ∣I n , R n ) and ϱ( T ∣I n , G n ) denote the Rademacher and Gaussian cotype 2 norm of T computed with n vectors, respectively. It is shown that the sequence ϱ( T ∣I n , R n ) has submaximal behaviour if and only if ϱ( T ∣I n , G n ) has. This means that ϱ ( T | I n , R n ) = o ( n ) ⇔ Q ( T | I n , G n ) = o (n 1 + log n) .Moreover, the class of these operators coincides with the class of operators preserving copies ofl ∞ nuniformly. The tool connecting these concepts is the equal norm Rademacher cotype of operators.