Polynomials in operator space theory
详细信息 查看全文
- 作者：Andreas Defant defant@mathematik.uni-oldenburg.de" class="auth_mail ; Dirk Wiesner
- 关键词：Operator spaces ; Completely bounded mappings ; Matrices ; Polynomials ; Multilinear mappings ; Tensor products
- 刊名：Journal of Functional Analysis
- 出版年：1 May, 2014
- 年：2014
- 卷：266
- 期：9
- 页码：5493-5525
- 全文大小：425 K
文摘
The aim of this article is to start a metric theory of homogeneous polynomials in the category of operator spaces. For this purpose we take advantage of the basic fact that the space of all m-homogeneous polynomials on a vector space E can be identified with the algebraic dual of the m-th symmetric tensor product . Given an operator space V, we study several different types of completely bounded polynomials on V which form the operator space duals of endowed with related operator structures. Of special interest are what we call Haagerup, Kronecker, and Schur polynomials - polynomials associated with different types of matrix products.