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Functional Analysis
Theorem: Let X be normed liner space over a filed K and Let X' be its dual space of X. If X' is separable then X is separable
Functional Analysis
Show that (C[a, b], ||f||2) is a norm
Functional Analysis
You have given a function λ : R → R with the following properties (x ∈ R, n ∈ N):
λ(n) = 0 , λ(x + 1) = λ(x) , λ(n+1/2)=1
Find two functions p, q : R → R with q(x)6=0 for all x such that λ(x) = q(x)(p(x) + 1).
λ(n) = 0 , λ(x + 1) = λ(x) , λ(n+1/2)=1
Find two functions p, q : R → R with q(x)6=0 for all x such that λ(x) = q(x)(p(x) + 1).
Functional Analysis
Every Hilbert space has an orthonormal basis.
Functional Analysis
In a Banach space, show that every absolutely convergent series is convergent.
Functional Analysis
Let X is Banach space and Let M be a subspace of X. Than M is itself a Banach space (using the norm from X) if and only if M is closed.
Functional Analysis
Lex X be an inner product space over R. If x ,y∈ X are such that ||x + y||=||x-y||then show that x ⊥ y.
Functional Analysis
Suppose that (xalpha)alpha element of j converges to x in X and (yalpha)alpha element of j converges to y in Y .show that (xalpha×yalpha) converges to x × y in X×Y
Functional Analysis
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
Functional Analysis
prove that a finite partially ordered set A has at least one maximal element
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#340153 on Dec 2023
#340153 on Dec 2023