Taiwanese Journal of Mathematics

STRONG CONVERGENCE THEOREMS FOR COMMUTATIVE SEMIGROUPS OF CONTINUOUS LINEAR OPERATORS ON BANACH SPACES

Kazutaka Eshita and Wataru Takahashi

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Abstract

We first prove a strong convergence theorem of Mann’s type for a commutative family of continuous linear operators in a Banach space by using strongly regular sequences of means on commutative semigroups. Using this, we obtain various strong convergence theorems for continuous linear operators in a Banach space.

Article information

Source
Taiwanese J. Math., Volume 9, Number 4 (2005), 531-550.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407882

Digital Object Identifier
doi:10.11650/twjm/1500407882

Mathematical Reviews number (MathSciNet)
MR2185401

Zentralblatt MATH identifier
1112.47006

Subjects
Primary: 47A35: Ergodic theory [See also 28Dxx, 37Axx] 47D03: Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20} 43A07: Means on groups, semigroups, etc.; amenable groups

Keywords
Banach space continuous linear operator commutative semigroup ergodic theorem iterative process mean strongly regular sequence

Citation

Eshita, Kazutaka; Takahashi, Wataru. STRONG CONVERGENCE THEOREMS FOR COMMUTATIVE SEMIGROUPS OF CONTINUOUS LINEAR OPERATORS ON BANACH SPACES. Taiwanese J. Math. 9 (2005), no. 4, 531--550. doi:10.11650/twjm/1500407882. https://projecteuclid.org/euclid.twjm/1500407882


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References

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