On the tensor product of unbounded quasi-representations of groups
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We prove that, in contrast to the case of the tensor product of two bounded quasi-representations, the tensor product of every quasi-representation T (of a group) admitting an invertible defect operator with an unbounded quasi-representation is not a quasi-representation. In particular, the tensor product of two quasi-representations of a group need not be a quasi-representation if one of the quasi-representations is unbounded.
Abstract
We prove that, in contrast to the case of the tensor product of two bounded quasi-representations, the tensor product of every quasi-representation T (of a group) admitting an invertible defect operator with an unbounded quasi-representation is not a quasi-representation. In particular, the tensor product of two quasi-representations of a group need not be a quasi-representation if one of the quasi-representations is unbounded.
참고문헌 (3)
- A. I. Shtern, "Quasisymmetry. I", Russ. J. Math. Phys, 2(3), pp.353~382 (1994)
- A. I. Shtern, "Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko’s conjecture", Fundam. Prikl. Mat, 13(7), pp.85~225 (2007)
- R. A. Ryan, "Introduction to Tensor Products of Banach Spaces. Springer Monographs in Mathematics" (2002), Springer-Verlag London, Ltd.