Exercise books on functional analysis

Solution 1:

Try Exercises in Functional Analysis by Constantin Costara and Dumitru Popa.

Solution 2:

The book M. Fabian, P. Habala, P. Hajek, V. Montesinos, V. Zizler: Banach Space Theory. The Basis of Linear and Nonlinear Analysis has plenty of exercises at the and of each chapter.

Google Books link, MR2766381 (2012h:46001), Zbl 1229.46001.

Solution 3:

There is the classic by Halmos, a problem book in Hilbert spaces. It is a GTM book so should be easy to find. Stein's Real Analysis and Functional Analysis might be also a good choice, if you want a broader flavor in analysis topics.

Why is the identity the only symmetric $0$-$1$ matrix with all eigenvalues positive?

Difference between imaginary and complex numbers

Using $\bigvee$ and $\bigwedge$ instead $\exists$ and $\forall$

How to find $\int_0^\pi (\log(1 - 2a \cos(x) + a^2))^2 \mathrm{d}x, \quad a>1$?

Tough Inverse Fourier Transform

How to show in a clean way that $z^4 + (x^2 + y^2 - 1)(2x^2 + 3y^2-1) = 0$ is a torus?

Column Space and SVD

How to prove that $\int_0^1 \exp\left(\frac{4x\sqrt{1-x^2}}{\sqrt{8x^2+1}}\right)\sqrt{\frac{1-8x^2+16x^4}{1+7x^2-8x^4}}dx=e-1$

Show that $K=K'$ if and only if $k=(\sqrt{2}-1)^2$ (Ahlfors)

Why the unit circle in $\mathbf{R^2}$ has one dimension?

Checking connectivity of adjacency matrix

Clarification for proof of $\mathbb{Q}$ being dense in $\mathbb{R}$ (Rudin's PMA)