Essential norms of weighted composition operators induced by automorphisms of the ball

Shan Li ()
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Shan Li: Jiangsu University of Technology

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 2, 663-670

Abstract: Abstract Let $$H_t$$ H t be the Hilbert spaces of holomorphic functions over the open unit ball $$\mathbb {B}_N$$ B N with reproducing kernels $$K_w(z) = (1-\langle z,w\rangle )^{-t}$$ K w ( z ) = ( 1 - ⟨ z , w ⟩ ) - t , where $$t\ge N$$ t ≥ N . This paper give estimates for the norms and essential norms of weighted composition operators induced by members in $$\text {Aut}(\mathbb {B}_N)$$ Aut ( B N ) on the Hilbert spaces $$H_t$$ H t . As applications, the boundedness and compactness of these weighted composition operators are characterized. Moreover, this paper gives estimates of the spectral radius and essential spectral radius of the above weighted composition operators.

Keywords: Weighted composition operator; Essential norm; Essential spectral radius; 47B33; 47B32 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00399-x

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