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prove that strong operator convergence implies weak operator convergence but converse is not true in general.



If a sub additive functional defined on a normed space X is nonnegative outside a sphere {x Illxll = r}, show that it is nonnegative for all x E X


prove that a finite partially ordered set A has at least one maximal element
Please, this is urgent , solve it as soon as possible.

Suppose V is finite-dimensional and phi is a linear functional on V. Then
there is a unique vector u in V such that
phi(v)=< v, u> for every v in V.
Show that norm is continuous function.

prove that

||u||>0 for u<>0


A metric space M is called a сomplete metric space if
Let TES^1. Prove that for all φES, (T*φ)^ = (2π)^(n/2)(φ-hat)(T-hat).
Let TES^1. Prove that for all φES, (T*φ)^ = (2π)^(n/2)(φ-hat)(T-hat).
Let TES^1. Prove that for all multi-indices a, (D^(a)T)^ = x^(a)T-hat.
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