Question

What are the conditions such that the banach apace satisfies the parallelogram law

Answer 1

Please make the word " Banach apace" clear.

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Answer 2

Answer:

Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well defined limit that is within the space. Banach spaces play a central role in functional analysis. Parallelogram law states that the sum of the squares of the length of the four sides of a parallelogram is equal to the sum of the squares of the length of the two diagonals. In Euclidean geometry, it is necessary that the parallelogram should have equal opposite sides.