Noncommutative L Structure Encodes Exactly Jordan Structure
نویسنده
چکیده
We prove that for all 1 ≤ p ≤ ∞, p 6= 2, the Lp spaces associated to two von Neumann algebrasM, N are isometrically isomorphic if and only if M and N are Jordan *-isomorphic. This follows from a noncommutative Lp Banach-Stone theorem: a specific decomposition for surjective isometries of noncommutative Lp spaces.
منابع مشابه
Structure Encodes Exactly Jordan Structure
We prove that for all 1 ≤ p ≤ ∞, p 6= 2, the L spaces associated to two von Neumann algebras M, N are isometrically isomorphic if and only if M and N are Jordan *-isomorphic. This follows from a noncommutative L Banach-Stone theorem: a specific decomposition for surjective isometries of noncommutative L spaces.
متن کاملThe James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces
Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...
متن کاملA Generalization of Noncommutative Jordan Algebras*
and x y denotes the product x ‘3~ = my + y.2’. In Section 1 we show that a noncommutative Jordan algebra of characteristic # 2 must satisfy (1). Since power-associative algebras satisfying (1) need not be flexible [5] it follows that the class of power-associative algebras satisfying (1) is strictly larger than the class of noncommutative Jordan algebras. In Section 2 we obtain a structure theo...
متن کاملNoncommutative jordan algebras with commutators satisfying an alternativity condition.
The theorems of this paper show that the main results in the structure and representation theory of Jordan algebras and of alternative algebras are valid for a larger class of algebras defined by simple identities which obviously hold in the Jordan and alternative cass. A new unification of the Jordan and associative theories is also achieved.
متن کاملConditional Probability, Three-Slit Experiments, and the Jordan Algebra Structure of Quantum Mechanics
Most quantum logics do not allow for a reasonable calculus of conditional probability. However, those ones which do so provide a very general and rich mathematical structure, including classical probabilities, quantum mechanics, and Jordan algebras. This structure exhibits some similarities with Alfsen and Shultz’s noncommutative spectral theory, but these twomathematical approaches are not ide...
متن کامل