Functional analysis Definition and 115 Threads

Does anyone know of where I should look to find lots of good functional analysis problems? I am currently reading Kreyszig which has great commentary, but the majority of the exercises are simple.

[SOLVED] Sequences in lp spaces... (Functional Analysis) Homework Statement Find a sequence which converges to zero but is not in any lp space where 1<=p<infinity. Homework Equations N/A The Attempt at a Solution I strongly suspect 1/ln(n+1) is a solution. Since ln(n+1) ->...

Hello I need help with an analysis proof and I was hoping someone might help me with it. The question is: Let (X,d) be a metric space and say A is a subset of X. If x is an accumulation point of A, prove that every r-neighbourhood of x actually contains an infinite number of distinct...

Hello Would anyone out there be able to help me with a problem I'm having? I have to prove that a function is open and that another is closed. The question is: Consider C [0,1] with the sup metric. Let f:[0,1]→R be the function given by f(x)=x²+2 Let A={g Є C[0,1]: d(g,f) > 3}. Prove...

Hello Would anyone out there be able to help me with a problem I'm having? I have to prove that a function is open and that another is closed. The question is: Consider C [0,1] with the sup metric. Let f:[0,1]→R be the function given by f(x)=x²+2 Let A={g Є C[0,1]: d(g,f) > 3}. Prove...

Hi! I was thinking about taking an introductory course in Functional analysis the commming spring, and was wondering if you more experienced guys can tell me if this is a good complement to understand theoretical quantum physics better? Cheers

first of all how do you write in latex

Suppose T: X -> Y and S: Y -> Z , X,Y,Z normed spaces , are bounded linear operators. Is there an example where T and S are not the zero operators but SoT (composition) is the zero operator?

I am thinking about taking a class on functional analysis. I am eventually planning on doing derivatives trading as a career. Is this class worth taking or should I try to find something more applied. I guess I am saying that I don't see how applied functional analysis is.

I have a commutative Banach algebra A with identity 1. If A contains an element e such that e^2 = e and e is neither 0 nor 1 (I think this also means to say that it contains a non-trivial idempotent), then the maximal ideal space of A is disconnected. Currently I am trying to show this but I...

Im trying to prove the following proposition Let (X,\|\cdot\|_X) and (Y,\|\cdot\|_Y) be normed vector spaces and let T:X \rightarrow Y be a surjective linear map. Then T is an isomorphism if and only if there exist m,M > 0 such that m\|x\|_X \leq \|Tx\|_Y \leq M\|x\|_X \quad \forall \, x...

Im having some difficulties proving some basic properties of the adjoint operator. I want to prove the following things: 1) There exists a unique map T^*:K\rightarrow H 2) That T^* is bounded and linear. 3) That T:H\rightarrow K is isometric if and only if T^*T = I. 4) Deduce that if T is...

Question 1 Prove that if (V, \|\cdot\|) is a normed vector space, then \left| \|x\| - \|y\| \right| \leq \|x-y\| for every x,y \in V. Then deduce that the norm is a continuous function from V to \mathbb{R}.

schröder's equation is a functional equation. let's assume A is a subset of the real numbers and g maps A to itself. the goal is to find a nonzero (invertible, if possible) function f and a real number r such that f\circ g=rf. motivation: if there is an invertible f, then the nth iterate...

hi! there is a good functional analysis book by Erwin Kreyzig...which has hilbert spaces and banach spaces and stuff!