Are Hahn-Banach extensions always unique? Justify.
In functional analysis, the Hahn-Banach theorem plays a fundamental role in extending linear functionals defined on a subspace to the entire space while preserving certain properties. The question of uniqueness in Hahn-Banach extensions ____ ______ ________ __________ ______.
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Define 3 3 A : C → C by A z( , z , z ) iz( , e z , z ) 2 3
Let A be an operator on a Hilbert space .H Show if Ax A x ∗ = for every ,H x ∈ then A is normal. Is it converse true? Justify
Let } u{ n be the sequence in l2 with 1 in the th n place and zeroes else where prove that the set } u{ n is an orthonormal basis for l 2
Prove that l1⊂ l2 If: T :(l2 ||.||)(l1,||.||2)
(l1,||.||2) is a compact operator, show that: T:,||.||
||.||2 is also compact.
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dt)t(xt is a bounded linear functional. Calculate
.
The space l3 is a Hilbert space