Looking for a rigorous intro to functional analysis with practical applications?

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Discussion Overview

The discussion revolves around recommendations for rigorous introductory texts on functional analysis, with a focus on both theoretical and practical applications. Participants share their preferences and inquire about the specific interests of the original poster.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • The original poster seeks a rigorous introduction to functional analysis, comparable to E.D. Bloch's book on real analysis.
  • One participant recommends several books, including Lang's "Real and Functional Analysis," Brezis's "Functional Analysis, Sobolev Spaces and PDE," Lax's "Functional Analysis," Reed-Simon's "Functional Analysis," and Conway's "A Course in Abstract Analysis."
  • Another participant asks whether the original poster is more interested in applications and examples or theoretical development.
  • The original poster expresses a preference for applications and indicates an interest in Lax's book due to its conciseness and breadth of topics.

Areas of Agreement / Disagreement

Participants generally agree on the importance of rigorous texts, but there are differing views on the balance between theoretical and practical applications, with no consensus on a single recommended book.

Contextual Notes

The discussion does not clarify specific assumptions regarding the level of prior knowledge or the exact nature of applications sought by the original poster.

Who May Find This Useful

Readers interested in functional analysis, particularly those seeking rigorous texts with practical applications or theoretical insights.

Andreol263
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Hello guys, can you recommend me a good and Rigorous introduction to functional analysis?? Rigorous like E.D.Bloch book on Real analysis if possible
 
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Here's some of the books I like

Lang's "Real and Functional analysis" https://www.amazon.com/dp/0387940014/?tag=pfamazon01-20
Brezis "Functional analysis, Sobolev spaces and PDE" https://www.amazon.com/dp/0387709134/?tag=pfamazon01-20
Lax "Functional analysis" https://www.amazon.com/dp/0471556041/?tag=pfamazon01-20
Reed-Simon "Functional Analysis" https://www.amazon.com/dp/0125850506/?tag=pfamazon01-20
Conway "A course in abstract analysis" https://www.amazon.com/dp/0821890832/?tag=pfamazon01-20
 
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Is your interest in applications and examples or more towards theoretical development? What would you like to do with it?
 
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More interest in applications actually.., Lax's Book appears to be pretty concise and have a hugh amount of topics, I'm going to try this book.
 

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