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Advances in Real and Complex Analysis with Applications pp 33–47Cite as

Birkhäuser

The Compact Approximation Property for Weighted Spaces of Holomorphic Mappings

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Abstract

In this paper, we examine the compact approximation property for the weighted spaces of holomorphic functions. We show that a Banach space E has the compact approximation property if and only if the predual \(\mathcal {G}_v(U)\) of the space \(H_v(U)\) consisting of all holomorphic mappings \(f:U\rightarrow \mathbb {C}\) (complex plane) with \(\sup \limits _{x\in U}v(x)\Vert f(x)\Vert <\infty \) has the compact approximation property, where v is a radial weight defined on a balanced open subset U of E such that \(H_v(U)\) contains all the polynomials. We have also studied the compact approximation property for the weighted (LB)-space VH(E) of holomorphic mappings and its predual VG(E) for a countable decreasing family V of radial rapidly decreasing weights on E.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, IIT Kanpur, Kanpur, 208016, India

    Manjul Gupta & Deepika Baweja

Authors
  1. Manjul Gupta
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  2. Deepika Baweja
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Correspondence to Manjul Gupta .

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Editors and Affiliations

  1. Department of Mathematics, Imperial College London, London, United Kingdom

    Michael Ruzhansky

  2. Department of Mathematics Education and the RINS, Gyeonsang National University, Jinju, Korea (Republic of)

    Yeol Je Cho

  3. Department of Mathematics, Anand International College of Engineering, Jaipur, Rajasthan, India

    Praveen Agarwal

  4. Departamento de Matemática Aplicada II, E.E. Aeronáutica e do Espazo, Universidade de Vigo, Ourense, Spain

    Iván Area

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Gupta, M., Baweja, D. (2017). The Compact Approximation Property for Weighted Spaces of Holomorphic Mappings. In: Ruzhansky, M., Cho, Y., Agarwal, P., Area, I. (eds) Advances in Real and Complex Analysis with Applications. Trends in Mathematics. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-10-4337-6_2

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