Uniform cross norms and tensor products of Banach algebras

Heredity of tensor products of topological algebras

“…The case of Banach algebras has been considered in [16], [4] and [5]. In this paper starting from a result of [5] we complete our previous result in [10] and also strengthen it to include the corresponding results of [4], [5] (cf. In this paper starting from a result of [5] we complete our previous result in [10] and also strengthen it to include the corresponding results of [4], [5] (cf.…”

“…The purpose of the present paper is to put into the context of the theory of tensor products of topological algebras [9], [10] some recent results concerning certain properties of permanence of a tensor product of Banach algebras [4], [5]. A brief report of the main results of this paper has been given in [11].…”

“…A brief report of the main results of this paper has been given in [11]. The case of Banach algebras has been considered in [16], [4] and [5]. The case of Banach algebras has been considered in [16], [4] and [5].…”

“…In particular, we are concerned with the question to what extent the tensor product (in an appropriate topology) of two semi-simple topological algebras is an algebra of the same kind; this seems to have a certain particular interest. A partial answer to this question (independently of [4], [5]) has been given in [10]. A partial answer to this question (independently of [4], [5]) has been given in [10].…”

Tensor product of Schaude bases

“…(4) This result is a generalization of the results for uniform crossnorms contained in [2]. It is still unknown whether the completion under an arbitrary crossnorm of the tensor product of two Banach spaces with bases has a basis.…”