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<p>In this paper, we formulate conditions for a pair of Fréchet spaces to be nonisomorphic. These conditions are formulated in terms of invariant classes of the spaces (<i>D</i><sub>1</sub>) and (<i>D</i><sub>2</sub>). As a consequence, we prove that weighted spaces of continuous functions of a special form are nonisomorphic. These spaces can be considered as a modification of spaces of power series of finite and infinite type.</p>

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Conditions for the Nonisomorphism of a Pair of Weighted Spaces of Continuous Functions

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • M. A. Shubarin

摘要

In this paper, we formulate conditions for a pair of Fréchet spaces to be nonisomorphic. These conditions are formulated in terms of invariant classes of the spaces (D1) and (D2). As a consequence, we prove that weighted spaces of continuous functions of a special form are nonisomorphic. These spaces can be considered as a modification of spaces of power series of finite and infinite type.