Elementary Proofs of Grothendieck Theorems for Completely Bounded Norms
نویسندگان
چکیده
We provide alternative proofs of two recent Grothendieck theorems for jointly completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko [PS02] and Haagerup and Musat [HM08]. Our proofs are elementary and are inspired by the so-called embezzlement states in quantum information theory. Moreover, our proofs lead to quantitative estimates.
منابع مشابه
Computing the Norms of Elementary Operators
We provide a direct proof that the Haagerup estimate on the completely bounded norm of elementary operators is best possible in the case of B(H) via a generalisation of a theorem of Stampfli. We show that for an elementary operator T of length `, the completely bounded norm is equal to the k-norm for k = `. A C*-algebra A has the property that the completely bounded norm of every elementary ope...
متن کاملSemidefinite Programs for Completely Bounded Norms
The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate proofs of some known facts about them.
متن کاملSection 3.2 - Cohomology of Sheaves
In this note we define cohomology of sheaves by taking the derived functors of the global section functor. As an application of general techniques of cohomology we prove the Grothendieck and Serre vanishing theorems. We introduce the Čech cohomology and use it to calculate cohomology of projective space. The original reference for this material is EGA III, but most graduate students would proba...
متن کاملNew proofs of Rosenthal’s l–theorem and the Josefson–Nissenzweig theorem
We give elementary proofs of the theorems mentioned in the title. Our methods rely on a simple version of Ramsey theory and a martingale difference lemma. They also provide quantitative results: if a Banach space contains l only with a bad constant then every bounded sequence admits a subsequence which is “nearly” a weak Cauchy sequence.
متن کاملShort Proofs of Two Basic Properties of Central Projections
In this note we prove two important properties of central projections, stated as Theorems A and B. They can be applied to obtain simple solutions of many hard problems in Euclidean geometry: for numerous examples see Yaglom [1, Ch. 1.3]. The proofs of these properties that I found in the literature were of two kinds: those which were completely elementary, assumed proficiency with Euclidean geo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012