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Generalized Cesàro Matrices

Published online by Cambridge University Press:  20 November 2018

H. C. Rhaly Jr
H. C. Rhaly Jr*
Affiliation:
Department of Mathematics, University of Mississippi, University, Mississippi 38677
*
Current Address: Department of Mathematics, Millsaps College, Jackson, Mississippi 39210
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Abstract

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For α ∈ [0, 1] the operator is the operator formally defined on the Hardy space H2 by

If α = 1, then the usual identification of H2 with l2 takes A1 onto the discrete Cesàro operator. Here we see that {Aα: α ∈ [0, 1]} is not arcwise connected, that Re Aα ≥ 0, that Aα is a Hilbert-Schmidt operator if α ∈[0, 1), and that Aα is neither normaloid nor spectraloid if α ∈(0, 1).

Keywords

47B9947A1247B1047B38Cesàro operatorHilbert-Schmidt operatornumerical range
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 4 , 01 December 1984 , pp. 417 - 422
Copyright
Copyright © Canadian Mathematical Society 1984

References

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