Asymptotic and Partial Asymptotic Hankel Operators on $$H^2(mathbb{D}^n)$$ H 2 ( D n ) ) |
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Authors: | Gupta Anuradha Gupta Bhawna |
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Affiliation: | 1.Department of Mathematics, Delhi College of Arts and Commerce, Netaji Nagar, University of Delhi, Delhi, India;2.Department of Mathematics, University of Delhi, Delhi, India |
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Abstract: | In this paper, we generalize the concept of asymptotic Hankel operators on H2(D) to the Hardy space H2(Dn) (over polydisk) in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence. Meanwhile, we introduce ith-partial Hankel operators on H2(Dn) and obtain a characterization of its compactness for n > 1. Our main results include the containment of Toeplitz algebra in the collection of all strong partial asymptotic Hankel operators on H2(Dn). It is also shown that a Toeplitz operator with symbol φ is asymptotic Hankel if and only if φ is holomorphic function in L∞(Tn). |
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Keywords: | Hankel operator Asymptotic Hankel operator partial asymptotic Hankel operator ith-partial Hankel operator ith-partial big Hankel operator |
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