Some Applications of Spectral Analysis to Ergodic Theory

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Authors

  • Department of Mathematics, Nagpur University, University Campus, Amravati Road, Nagpur ,IN

Abstract

Let X be a Banach Space and L [X, X] the space of continuous linear operators on X. For T ∈ L [X, X] let An = 1/n (T+ T2 + . . . + Tn), n = l,2, ... To discuss the convergence properties of {An} when T is a compact operator, Higgins [2] used spectral decomposition and the properties of collectively compact sets of operators.

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Published

1974-12-01

How to Cite

Deshpande, M. V. (1974). Some Applications of Spectral Analysis to Ergodic Theory. The Journal of the Indian Mathematical Society, 38(1-4), 147–154. Retrieved from http://informaticsjournals.com/index.php/jims/article/view/16688

 

References

P. M. ANSELONE AND T. W. PALMER. Spectral analysis of collectively compact Strongly convergent operator sequences. Pac. Jour. Math. 25 (1963), 423-431.

J. A. HIGGINS. Collectively Compact Sets of Linear Operators. Ph. D. Dissertation, New Mexico State University, 1971.

N. E. JOSHI AND M. V. DESHPANDE. Collectively compact and semi-compact Sets of linear operators in topological vector spaces. Pac. Jour. Math. 42. (1973).

N. DUNFORD AND J. T. SCHWARTZ. Linear Operators. Part”I. Inter Science, New York, 1958.

K. YOSIDA. Functional Analysis. Springer Verlag, 1968.