I would like to ask for some recommendation of introductory texts on functional analysis. I am not a professional mathematician and I am totally new to the subject. However, I found out that some knowledge of functional analysis and operator theory would be quite helpful to my work…
What I am searching for is some accessible and instructive text not necessarily covering the subject in great depth, but explaining the main ideas. I am not searching for a text for engineers, some amount of mathematical rigor would be fine. But I found myself unable of reading some standard textbooks covering in great depth a large amount of issues in theory of Banach spaces, etc. I am looking for something that proceeds to the most important topics (e.g., spectral theory) faster than the most of textbooks, but not at the expense of rigor. I.e., something that covers rigorously the main topics, but concentrates only on the main ideas.
Simply an accessible introductory text for a fast orientation in the subject.
Moreover, I would prefer a text that does not require any background in measure theory and similar disciplines.
And another question: is there any functional analysis book that deals primarily with sequence spaces? It need not fulfill the description above.
Thank you for your recommendations!
Best Answer
I think that Kreyszig'book is a good introduction, though not very short.
Spaces of sequences are classical Banach spaces, and there are books that study their properties systematically. A classic book is this one. But also Larsen's book has plenty of examples from $\ell^p$, $c_0$, $c_{00}$.