er ... mkay .... Let's see....Diestel, Dunford and Schwartz, John B. Conway, Edmunds and Evans, Halmos, Akhiezer and Glazman, and Lindenstrauss and Tzafriri are in my corner on this one. Don't know who is in your corner. Of course, if needed I'll rope some other WMDs in from the university library, but these are the only ones I have on my shelf at home at the moment.I wasn't suggesting MathWorld as a source of detailed info. It is typically good for a quick definition though, and for honing down a prospective internet or citation search.

Greame, sigh ... you expect to much from that Drei-Quartel mathematican,he may call it a joke, learners may find it rather odd - especially afterthey got replies from their teachers ... and his cyclotomic nonsense isclose to asserting 'the earth is flat'.

Let me see if I have this correct --You AVt, Graeme, Diestel, Dunford and Schwartz, John B. Conway, Edmunds and Evans, Halmos, Akhiezer and Glazman, and Lindenstrauss and Tzafriri think that banach space is simply a linear vector space???I'd say you all don't have a clue. Actually you all don't have a clue whether I say so or not.Yes I am asserting 'the earth is locally flat'. Otherwise you wouldn't have a local diffusion for an exp map when solving problems usingstochastic differential geometry.Here's another folk idea: Brownian filterations can exist. No they can't exist. As Eric pointed out, Wiener (or Brownian) motion requires an ncg for noise generation. Diffusions must be in Hilbert space, but Hilbert space doesn't support any ncg. So is BM not a diffusion process? Actually not. It's only a diffusion process if sigma is exactly zero. The telltail sign again that BM is neither in Hilbert space nor a diffusion is the latent autocorrelation which is by definition cyclotomic.Why don't you check with a world class mathematician, like Jim Simons. He'll either say I'm right or say nothing to avoid releasing trade secrets.

AVt,Here's a special treat for you.Are there any prime numbers, per se, in banach space.No. Only primes as factors. Why? Every number must have 2 non-unity factors for the field to be cyclotomic. Of course, one and only one arbitary scaling factor is permitted (which can be any real number).As a side note, I think Fermat knew that when he scribbled in his margin.Newton Edit: Let's refer to Banach as the space without Hilbert space. If we mean hilbert space then we'll be explicit.

N,let me know when you release some trade secrets and publish your first book. Should be in a line with Andy Kaufman.

DDoom --I'm afraid you're the joke, today. Either add something intelligent or get the fuck lost.

QuoteOriginally posted by: GraemeDiestel, Dunford and Schwartz, John B. Conway, Edmunds and Evans, Halmos, Akhiezer and Glazman, and Lindenstrauss and Tzafriri are in my corner on this one.You might add: G. Folland "Real Analysis" p 144. Wiley (1984)C. Isham, Lecture notes for his course in Group Theory (1989)Regards,Niclas

nsande--I finished my graduate work in the late '70s and noticed many books on this topic as well as stochastic calc starting to be published. What theauthors usually failed to recognize is that sampling independent entities (as in queueing theory) is quite different than samples in time of a parameter of an entity. The latter almost always involves Wick ordering which requires the use of differential geometry to handle the cyclotomic, or twistor shape of the min action (geodesic) in state space. Folks in OR noticed these problem early on when looking at dynamic programming problems. Only in the last few years, I again encountered this folk math when I developed an interest in QF. Fat tails, smiles, etc are not a result of someweird financial distributions but rather crappy math by the authors you mention and many others.All these distinctions in the type of space, even when the pnorm is <1 (Gauss curvature between (0,-1] ) can be totally avoided by using SUSYcoordinates (orthogonal spinors in clifford algebra). If fact even Feynman loops become unnecessary.Newton

N,I can't belive that you have this much energy. You have consistently spouted this crap for 3 years. You are no more lucid than the first post of yours that I read (drunk) three years ago. This is the simplest question on earth: what is a banach space? simple. At the most you could talk about how it comes up in phynance, like L2 on omega x [0,inf) or something, but that is the most you could get from the question.

C3,This my friend is the 'crap' of RenTec. Those interested in the microstructure of markets are surely interested. Anyway, I never met a physicist who wasn't a piece of sh!t mathematician, so your comments are taken in that light.Didn't you ever wonder what causes smiles or why BS diffusions aren't accurate and require fudging by traders. How Simons makes his money? Why all financial time series have autocorrelation when BS diffusions imply they can't. What causes the Slutsky effect whentimeseries trend differencing? What's the solution to Nonius' E(exp(LAM)) problem (or perhaps not a two but an n-entity CDO problem) Or why FX timeseries volatility adds like entropy rather than like independent normal dist rv ticks.

Correct definition time and salient characteristics:What's Banach space: a space which has a pnorm that's <infinity, >1 but !=2. This metric space has coordinates drawn from a cyclotomic field determined by the pnorm. It does not support the inner product. Levy distributions are produced by the projection of trajectories onto hilbert space. This space is Wick ordered (index theorm in topology).Hilbert space is a single norm metric space where the pnorm = 2. It supports the inner product. No is ordering in this space.In differential geometry, the global coordinates are always in Hilbert space. Local coordinates are in Banach space. When there is a trivalization there is only a hilbert space. What's the relationship of this jazz to finance. It's the infrasturcture necessary to correctly solve problems in finance. Or perhaps understandreturn distributions.

QuoteOriginally posted by: NC3,This my friend is the 'crap' of RenTec. Those interested in the microstructure of markets are surely interested. Anyway, I never met a physicist who wasn't a piece of sh!t mathematician, so your comments are taken in that light.Didn't you ever wonder what causes smiles or why BS diffusions aren't accurate and require fudging by traders. How Simons makes his money? Why all financial time series have autocorrelation when BS diffusions imply they can't. What causes the Slutsky effect whentimeseries trend differencing? What's the solution to Nonius' E(exp(LAM)) problem (or perhaps not a two but an n-entity CDO problem) Or why FX timeseries volatility adds like entropy rather than like independent normal dist rv ticks.You're right.

C3--You can't just say 'You're right." and get away with it.

You are right.

I think I got it.N's real name has to be Bogdanov.Regards,Niclas