Assume  that $H$ is  a  separable Hilbert space.
Is there a polynomial $p(z)\in \mathbb{C}[x]$ with $deg(p)&gt;1$ with the following property?:

Every densely defined operator $A:D(A)\to D(A),\;D(A)\subset H$  with $p(A)=0$ is  necessarily  a  bounded operator on $H$.

That is the polynomial-operator equation $p(A)=0$ has only bounded solution.


Question: Need directions regarding the learning process I should follow for learning Photoshop
Answer: Experiment a lot, test out all those buttons and functions one by one, read tutorials, try them out, bring your knowledge over from Gimp such as how to use layers, repeat.

You can always buy a book and test out the techniques there, but unless you aim to become a 100% graphic designer I will recommend you to keep it simple at first, more related to what your purpose with it is.

(the cartoon you link to is probably made with Illustrator though)

Edit: if you specifically want to this for web design, check also Adobe Fireworks which is more targeted towards web design than PS is.