Commutants for some classes of Hausdorff matrices

Author:
B. E. Rhoades

Journal:
Proc. Amer. Math. Soc. **123** (1995), 2745-2755

MSC:
Primary 40G05; Secondary 40C05

DOI:
https://doi.org/10.1090/S0002-9939-1995-1301525-5

MathSciNet review:
1301525

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the algebra of all bounded infinite matrices on *c*, the space of convergent sequences, the subalgebra of consisting of lower triangular matrices. It is well known that, if *H* is any Hausdorff matrix with distinct diagonal entries, then the commutant of *H* in contains only Hausdorff matrices. In previous work the author has shown that a necessary condition for the commutant of a Hausdorff matrix *H* to be the same in and is that *H* have distinct diagonal entries, but that the condition is not sufficient. In this paper it is shown that certain Hausdorff matrices, with distinct diagonal entries, have the same commutants in and .

**[1]**Stephen Barnett,*Polynomials and linear control systems*, Monographs and Textbooks in Pure and Applied Mathematics, vol. 77, Marcel Dekker, Inc., New York, 1983. MR**704016****[2]**Felix Hausdorff,*Summationsmethoden und Momentfolgen. I*, Math. Z.**9**(1921), no. 1-2, 74–109 (German). MR**1544453**, https://doi.org/10.1007/BF01378337**[3]**J. D. Hill,*On perfect methods of summability*, Duke Math. J.**3**(1937), no. 4, 702–714. MR**1546024**, https://doi.org/10.1215/S0012-7094-37-00358-2**[4]**A. Jakimovski,*The product of summability methods*:*New classes of transformations and their properties*, Tech. Note Contract AF 61 (052)-187, U.S. Air Force.**[5]**B. Kuttner and M. R. Parameswaran,*Matrices that commute with*, preprint.**[6]**B. E. Rhoades,*Commutants of some Hausdorff matrices*, Pacific J. Math.**42**(1972), 715–719. MR**0316931****[7]**B. E. Rhoades,*Correction to: “Commutants of some Hausdorff matrices” (Pacific J. Math. 42 (1972), 715–719)*, Pacific J. Math.**49**(1973), 617–619. MR**0364939****[8]**B. E. Rhoades and A. Wilansky,*Some commutants in 𝐵(𝑐) which are almost matrices*, Pacific J. Math.**49**(1973), 211–217. MR**0336437****[9]**L. L. Silverman and J. D. Tamarkin,*On the generalization of Abel's theorem for certain definitions of summability*. Math. Z.**29**(1928), 161-170.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1301525-5

Keywords:
Cesàro,
commutant,
Euler,
Hausdorff matrices,
Hölder

Article copyright:
© Copyright 1995
American Mathematical Society