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LOWER BOUNDS OF OPERATORSON WEIGHTED [Lscr ]P SPACES AND LORENTZ SEQUENCE SPACES

Published online by Cambridge University Press:  01 May 2000

G. J. O. JAMESON  and
R. LASHKARIPOUR
G. J. O. JAMESON
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, Great Britain. E-mail: [email protected]
R. LASHKARIPOUR
Affiliation:
Faculty of Science, University of Sistan and Baluchistan, Zahedan, Iran. E-mail: [email protected]
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Abstract

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The problem considered is the determination of “lower bounds” of matrix operators on the spaces\ell_p(w) or d(w,p). Under fairly general conditions, the solution is the same for both spaces and is given by the infimum of a certain sequence. Specific cases are considered, with the weighting sequence defined by w_n = 1/n^\alpha . The exact solution is found for the Hilbert operator. For the averaging operator, two different upper bounds are given, and for certain values of p and \alpha it is shown that the smaller of these two bounds is the exact solution.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 2 , May 2000 , pp. 211 - 223
Copyright
2000 Glasgow Mathematical Journal Trust