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<p>We introduce the <i>q</i>-tensor product of semi-closed operators. Related basic properties between algebraic tensor products, tensor products and <i>q</i>-tensor products are studied. The <i>q</i>-tensor product of semi-closed or closed projections is considered. It is shown that the tensor product can be defined for ‘non-densely defined’ closable operators using properties of <i>q</i>-tensor products. As applications, we investigate relations between (<i>q</i>-) tensor products and the Krein—von Neumann extension of a semi-closed positive symmetric operator with the positively closable condition.</p>

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Tensor products of semi-closed operators and applications

  • 期刊论文

  • 发表日期：

    2025年9月4日

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  • Go Hirasawa

摘要

We introduce the q-tensor product of semi-closed operators. Related basic properties between algebraic tensor products, tensor products and q-tensor products are studied. The q-tensor product of semi-closed or closed projections is considered. It is shown that the tensor product can be defined for ‘non-densely defined’ closable operators using properties of q-tensor products. As applications, we investigate relations between (q-) tensor products and the Krein—von Neumann extension of a semi-closed positive symmetric operator with the positively closable condition.