Tensor Banach algebras of projective type. II. The $l_1$ case

V. D. Ivashchuk

Scientific and Research Centre on Surface and Vacuum Properties Investigations

Abstract: It is shown that the tensor Banach functor of projective type $\widehat{\mathscr T}_K$ [1] corresponding to the complete normed field $K$ is quasiidempotent on infinite-dimensional $l_1$ spaces, i.e.,
$$ \widehat{\mathscr T}_K(\theta_K(\widehat{\mathscr T}_K(l_1(M,K))))\cong\widehat{\mathscr T}_K(l_1(M,K)), $$
where $M$ is an infinite set and $\theta_K$ is the forgetful functor. An $l_1$ realization of the Banach algebra $\widehat{\mathscr T}_K(l_1(M,K))$ is constructed.

Received: 21.09.1991

 English version: Theoretical and Mathematical Physics, 1992, 91:2, 462–473

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