scholarly journals Real Positive Maps and Conditional Expectations on Operator Algebras

2021 ◽  
pp. 63-102
Author(s):  
David P. Blecher
Keyword(s):  
Operator Algebras ◽  
Positive Maps ◽  
Conditional Expectations

scholarly journals A class of operator algebras induced by probabilistic conditional expectations.

1993 ◽  
Vol 40 (2) ◽  
pp. 359-376 ◽  
Author(s):  
Alan Lambert ◽  
Barnet M. Weinstock
Keyword(s):  
Operator Algebras ◽  
Conditional Expectations

scholarly journals Effect algebras with state operator

10.29007/jbdq ◽  
2018 ◽  
Author(s):  
Silvia Pulmannova
Keyword(s):  
Effect Algebra ◽  
Operator Algebras ◽  
Internal State ◽  
Effect Algebras ◽  
State Operator ◽  
Conditional Expectations ◽  
Definition Of ◽  
Mv Algebras

A state operator on effect algebras is introduced as an additive, idempotent and unital mapping from the effect algebra into itself. The definition is inspired by the definition of an internal state on MV-algebras, recently introduced by Flaminio and Montagna. We study state operators on convex effect algebras, and show their relations with conditional expectations on operator algebras.

scholarly journals Real Operator Algebras and Real Positive Maps

2021 ◽  
Vol 93 (5) ◽  
Author(s):  
David P. Blecher ◽  
Worawit Tepsan
Keyword(s):  
Operator Algebras ◽  
Positive Maps

Contractive projections and real positive maps\cr on operator algebras

2021 ◽  
Vol 256 (1) ◽  
pp. 21-60
Author(s):  
David P. Blecher ◽  
Matthew Neal
Keyword(s):  
Operator Algebras ◽  
Positive Maps ◽  
Contractive Projections

scholarly journals Conditional Expectations for Unbounded Operator Algebras

2007 ◽  
Vol 2007 ◽  
pp. 1-22 ◽  
Author(s):  
Atsushi Inoue ◽  
Hidekazu Ogi ◽  
Mayumi Takakura
Keyword(s):  
Hilbert Space ◽  
Conditional Expectation ◽  
Unbounded Operator ◽  
Operator Algebras ◽  
Linear Map ◽  
Conditional Expectations ◽  
Positive Linear Map

Two conditional expectations in unbounded operator algebras (O∗-algebras) are discussed. One is a vector conditional expectation defined by a linear map of anO∗-algebra into the Hilbert space on which theO∗-algebra acts. This has the usual properties of conditional expectations. This was defined by Gudder and Hudson. Another is an unbounded conditional expectation which is a positive linear mapℰof anO∗-algebraℳonto a givenO∗-subalgebra𝒩ofℳ. Here the domainD(ℰ)ofℰdoes not equal toℳin general, and so such a conditional expectation is called unbounded.

scholarly journals W algebras, cosets and VOAs for 4d $$ \mathcal{N} $$ = 2 SCFTs from M5 branes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Dan Xie ◽  
Wenbin Yan
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Nilpotent Orbit ◽  
Vertex Operator Algebras ◽  
Flavor Symmetries ◽  
Conformal Embedding

Abstract We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general $$ \mathcal{N} $$ N = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.

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