The Journal of the Indian Mathematical Society

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On the Existence of a Norm Weaker than a Given Family of Norms on a Vector Space


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1 S. V. University, Tirupati, India
     

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Let Ni(x) be a sequence of norms defined over a vector space E. Let us consider all those linear topologies T over E which are weaker than Ni(x) for all i. (For brevity Ni(x) is used to denote the norm as well as the corresponding topology). These include the lattice product tolopogy [3] of the Ni(x), i.e. the strongest topology weaker than each of the Ni(x) topologies.
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  • On the Existence of a Norm Weaker than a Given Family of Norms on a Vector Space

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Authors

M. V. Subba Rao
S. V. University, Tirupati, India

Abstract


Let Ni(x) be a sequence of norms defined over a vector space E. Let us consider all those linear topologies T over E which are weaker than Ni(x) for all i. (For brevity Ni(x) is used to denote the norm as well as the corresponding topology). These include the lattice product tolopogy [3] of the Ni(x), i.e. the strongest topology weaker than each of the Ni(x) topologies.