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On operators of class (N, k)

Published online by Cambridge University Press:  24 October 2008

P. B. Ramanujan
P. B. Ramanujan
Affiliation:
Sardar Patel University, Vallabh Vidyanagar, India
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Extract

Istrăţescu (2) has introduced a class of operators on a Banach space called operators of class (N, k). An operator T (a bounded linear transformation) on a Banach space X is said to be an operator of class (N, k), k = 2, 3,…, if ‖Tx‖k ≤ ‖Tkx‖ for all x ∈ X such that ‖x‖ = 1. If k = 2, such an operator is called an operator of class (N)(3). If X is a Hilbert space, then the class of operators of class (N) on X is an extension of the class of hyponormal operators on X (3). The object of this note is to generalize to operators of class (N, k) on a Banach space X, some results which are known to be true for normal operators on a Hilbert space, particularly with regard to their ascent and descent.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 141 - 142
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

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