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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Subnormal generalized Hausdorff operators


Authors: B. K. Ghosh, B. E. Rhoades and D. Trutt
Journal: Proc. Amer. Math. Soc. 66 (1977), 261-265
MSC: Primary 40C05; Secondary 47B20
MathSciNet review: 0467068
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Abstract: One type of generalized Hausdorff matrix is the lower triangular matrix with entries $ {h_{nk}} = (_{n - k}^{n + \alpha }){\Delta ^{n - k}}{\nu _k}$, where $ \Delta {\nu _n} = {\nu _n} - {\nu _{n + 1}},{\nu _n} = \smallint _0^1{t^{n + \alpha }}d\beta (t)$ for some $ \beta (t)$ of bounded variation on [0, 1] and for some $ \alpha \geqslant 0$. The matrix $ {H_\alpha }$ generated by $ {\nu _n} = {(n + \alpha + 1)^{ - 1}}$ is shown to be a subnormal operator on $ {l^2}$ if $ \alpha $ is a nonnegative integer.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0467068-5
PII: S 0002-9939(1977)0467068-5
Article copyright: © Copyright 1977 American Mathematical Society