Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories accessible adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology newpage nlab noncommutative noncommutative-geometry number number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorAndrew Stacey
    • CommentTimeNov 1st 2010

    After getting myself confused about the distinction between the various notions of basis in infinite dimensions, I wrote up my attempt to disentangle myself at basis in functional analysis (also redirects from Hamel basis, topological basis, and Schauder basis. Hmm, now I think about it, maybe “topological basis” is too close to “basis of a topology”). I may still be confused about stuff, of course.

    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeNov 1st 2010
    • (edited Nov 1st 2010)

    @Andrew and others: I note that C*-algebras are not included in the contents of Functional Analysis. Is there a reason for this? I would have thought that was a relevant entry, but classification of a topic under a particular heading is often a question of taste.

    • CommentRowNumber3.
    • CommentAuthorAndrew Stacey
    • CommentTimeNov 1st 2010
    • (edited Nov 1st 2010)

    As far as I’m concerned there’s no reason for this. I think that it’s just historical. The C *C^*-algebra pages were around before the functional analysis ones, and it’s a bigger topic (in terms of weight of nlab-pages). I wrote the original contents and I’m much less aware of C *C^*-algebras than most functional analysis people are (probably because I’m not a true functional analyst).

    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeNov 1st 2010

    Hmm, now I think about it, maybe “topological basis” is too close to “basis of a topology”

    Indeed, topological basis already redirects to topological base.

    Personally, I would like to have it redirect to your article; I never use ‘basis’ to mean a base. But it’s clear that other contributors to the nLab, particularly Urs, do use ‘basis’ to mean a base for a topology.

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeNov 3rd 2010
    • (edited Nov 3rd 2010)

    2 and 3 (Tim and Andrew): The entry on functional analysis mentions operator algebras which in turn contain C C^\star-algebras. The top contents page of Mathematics in nnlab has operator algebras and functional analysis as separate subjects and I think it is OK. While operator algebras have heavy analysis content much of the research is about structural porperties similar and partly motivated by theorems in areas like ring theory. Description of many math departements and of many multidisciplinary conferences have them separately while some have them together. I think it is practical to emphasis each separately in nlab while each should have mention of the other inside. I see no problem with that.

    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeNov 3rd 2010

    The entry functional analysis - contents does not mention operator algebras nor c-star algebras not links with non-comm geom. There is a category:functional analysis, but only one entry under it, and so on. I was just curious about whether C-star algebras were still considered as part of Funct. Anal. as in the good old days of Simmons book which I used for spectral theory and Banach Algebras as a student. More seriously, and Zoran I think you are much more expert on this than me, should there be some greater amount of structure used to collect up the Funct. Anal. stuff. (Also Stuff on shape in Funct. Anal. could be separated off… but that is another direction. What do you think?

    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeNov 3rd 2010
    • (edited Nov 3rd 2010)

    Oh, I have not been aware of that contents page, just functional analysis, where operator algebras are mentioned. I will add operator algebras and spectral theory there. I agree that eventually the special topics like the algebraic theories in this setup could be separated off. At this moment, there is too little functional analysis in nlab anyway (big areas like e.g. “operator spaces” are missing) so some weird extras can feature for a bit, until a more systematic list is collected and realized in nlab. I think that counting operator algebras as part of functional analysis in this or that level of strictness depends on practioner.

    • CommentRowNumber8.
    • CommentAuthorTim_Porter
    • CommentTimeNov 3rd 2010

    Entries on non-commutative geometry will probably need organising, but that is a very diverse area ’out there’ beyond the Lab, so perhaps we should wait and see the growth. I am having discussions with people at Cardiff about exactly that area, and there would seem to be some interesting developments coming soon. I hope they come off!

    • CommentRowNumber9.
    • CommentAuthorzskoda
    • CommentTimeNov 3rd 2010

    I hope you explained them that having collectively improving but permanent online notes is useful aid to work, rather than predominantly an altruistic task. People are afraid that they will be loosing time working in nlab. While I had been hurted myself by not restraining from that work in crictial moments; in long run and distributing the “work” more wisely within contributor’s own time, and more functionally as part of one’s own endeavors, one saves time, we believe.

    • CommentRowNumber10.
    • CommentAuthorTim_Porter
    • CommentTimeNov 3rd 2010

    I do not get paid for doing research anyway so it makes no difference from that point of view, but you are right n-Lab activities do provide a very valuable aid to research… except I seem to try to do far too many things at once! :-(

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)