Ergodic projections of continuous and discrete semigroups

Author:
Sen-Yen Shaw

Journal:
Proc. Amer. Math. Soc. **78** (1980), 69-76

MSC:
Primary 47A35; Secondary 47D05

DOI:
https://doi.org/10.1090/S0002-9939-1980-0548087-7

MathSciNet review:
548087

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *X* be a Banach space. Let be a uniformly bounded semigroup of operators on *X*, which converges strongly to *P*, known to be a projection, as *t* goes to 0. If *A* is its generator and [resp., ] is the set of *x* for which

*X*is reflexive. Some results on relations among the projections , are obtained. In particular, we have for all sufficiently small

*t*if

*A*is bounded.

**[1]**P. L. Butzer and H. Berens,*Semi-groups of operators and approximation*, Springer-Verlag, New York, 1967. MR**0230022 (37:5588)****[2]**J. A. Goldstein, C. Radin and R. E. Showalter,*Convergence rates of ergodic limits for semigroups and cosine functions*, Semigroup Forum**16**(1978), 89-95. MR**0487585 (58:7204)****[3]**E. Hille and R. S. Phillips,*Functional analysis and semigroups*, Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc., Providence, R. I., 1957. MR**0089373 (19:664d)****[4]**S. C. Lin and S. Y. Shaw,*Ergodic theorems of semigroups and application*, Bull. Inst. Math. Academia Sinica**6**(1978), 181-188. MR**0493508 (58:12508)****[5]**D. V. Widder,*An introduction to transform theory*, Academic Press, New York, 1971.**[6]**K. Yosida,*Functional analysis*, Springer-Verlag, New York, 1970.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0548087-7

Keywords:
Semigroups of operators,
mean ergodic theorem,
ergodic projections,
infinitesimal generator

Article copyright:
© Copyright 1980
American Mathematical Society