Functional analysis with worked examples

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Discussion Overview

The discussion centers around the search for introductory functional analysis books that include calculus examples to illustrate various axioms. Participants share their experiences with different texts and express opinions on the accessibility and abstract nature of functional analysis.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants recommend Kreyszig's book as a friendly introduction to functional analysis, though it is noted to be somewhat abstract.
  • One participant emphasizes that functional analysis is inherently abstract, serving to generalize concepts from linear algebra and analysis, and suggests that a background in linear algebra is necessary for studying it.
  • Another participant mentions Robert Geroch's "Mathematical Physics" as a good introduction, particularly the last two chapters, but expresses uncertainty about the availability of worked examples.
  • There is a critique regarding the abstraction in functional analysis, with a participant noting that the term "abstract" implies derivation from concrete concepts, and mentions Dieudonné's "History of Functional Analysis" as a potential resource, albeit incomplete and less readable.

Areas of Agreement / Disagreement

Participants generally agree on the abstract nature of functional analysis and the challenges it presents, but there is no consensus on the best introductory texts that include worked examples.

Contextual Notes

Some participants express limitations in the available resources, particularly regarding the balance between abstraction and concrete examples in functional analysis literature.

bugatti79
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Folks

Are there any introductory functional analysis books which show calculus examples to illustrate the different axioms?

thanks
 
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I always though Kreyszig's book was outstanding.
 
daveb said:
I always though Kreyszig's book was outstanding.

Yes, I have that. Its still a bit abstract...:-)
 
bugatti79 said:
Yes, I have that. Its still a bit abstract...:-)

Functional analysis itself is abstract; being abstract is its entire purpose (it generalizes many of the objects studied in linear algebra and analysis). Really, Kreyszig is one of the friendliest introductions you're going to find. You really shouldn't be studying it without a background in linear algebra anyway.
 
Last edited:
ok,

Thanks
 
Robert Geroch, Mathematical Physics. Last 2 chapters. Best intro to functional I have seen. I don't know about worked examples. There are some very good examples, but also very nice proofs.

The point of functional might be to be abstract, but the word abstract is a verb. Things should be abstracted FROM something. Unfortunately, I'm not aware of any functional analysis book that keeps that in mind quite as much as they ought to, except maybe Dieudonne's History of Functional Analysis, but it is not very complete or readable.
 
homeomorphic said:
Robert Geroch, Mathematical Physics. Last 2 chapters. Best intro to functional I have seen. I don't know about worked examples. There are some very good examples, but also very nice proofs.

The point of functional might be to be abstract, but the word abstract is a verb. Things should be abstracted FROM something. Unfortunately, I'm not aware of any functional analysis book that keeps that in mind quite as much as they ought to, except maybe Dieudonne's History of Functional Analysis, but it is not very complete or readable.

Ok cheers
 

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