Dear all,(adsbygoogle = window.adsbygoogle || []).push({});

I'm reading the tensor part of "A course in modern mathematical physics" by Szekeres and I have trouble understanding a concept that you can find in the attached image of the book page. What are the elements of F(V)? If my understanding of (external) direct sums of vector spaces is correct, the elements of F(V) are arrays of an infinite number components, where each element j of the array is an element of the tensor product of j copies of V. Then, how is the subsequent formal finite formal sum for the typical member of F(V) justified? I'm sure I'm missing some details, perhaps I can't see identifications etc.

Thanks for your help.

Goldbeetle

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# Infine Direct Sum of Vector spaces

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