IJPAM: Volume 100, No. 1 (2015)

DECOMPOSABILITY OF NONNEGATIVE $r$-POTENT
OPERATORS ON $\mathcal{L}^2(\mathcal{X})$

Rashmi Sehgal Thukral$^1$, Alka Marwaha$^2$
$^{1,2}$Department of Mathematics
Jesus and Mary College
University of Delhi
Chanakyapuri, New Delhi, 110021, INDIA


Abstract. We investigate the decomposability of nonnegative compact $r$-potent operators on a separable Hilbert space $\mathcal{L}^2(\mathcal{X})$. We provide a constructive algorithm to prove that basis functions of range spaces of nonnegative $r$-potent operators can be chosen to be all nonnegative and mutually orthogonal. We use this orthogonality to establish that nonnegative compact $r$-potent operators with range spaces of dimension strictly greater than $r-1$ are decomposable.

Received: October 16, 2014

AMS Subject Classification: 47A15, 47B07

Key Words and Phrases: decomposition, $r$-potent operators, compact

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DOI: 10.12732/ijpam.v100i1.4 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 100
Issue: 1
Pages: 29 - 52


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