scholarly journals Open projections do not form a right residuated lattice

10.29007/61zj ◽  
2018 ◽  
Author(s):  
David Kruml
Keyword(s):  
Residuated Lattice ◽  
C Algebra ◽  
Compatible Elements ◽  
Monoid Structure

The lattice of open projection of a C*-algebra has a partial monoid structure on compatible elements. However, this does not extend to a total right residuated operation.

scholarly journals THE STRUCTURE OF RESIDUATED LATTICES

2003 ◽  
Vol 13 (04) ◽  
pp. 437-461 ◽  
Author(s):  
KEVIN BLOUNT ◽  
CONSTANTINE TSINAKIS
Keyword(s):  
Residuated Lattice ◽  
Residuated Lattices ◽  
Binary Operations ◽  
Residuated Structures ◽  
Structure Formula ◽  
Left And Right ◽  
The Right ◽  
Decomposition Theorems ◽  
First Time ◽  
Monoid Structure

A residuated lattice is an ordered algebraic structure [Formula: see text] such that <L,∧,∨> is a lattice, <L,·,e> is a monoid, and \ and / are binary operations for which the equivalences [Formula: see text] hold for all a,b,c ∈ L. It is helpful to think of the last two operations as left and right division and thus the equivalences can be seen as "dividing" on the right by b and "dividing" on the left by a. The class of all residuated lattices is denoted by ℛℒ The study of such objects originated in the context of the theory of ring ideals in the 1930s. The collection of all two-sided ideals of a ring forms a lattice upon which one can impose a natural monoid structure making this object into a residuated lattice. Such ideas were investigated by Morgan Ward and R. P. Dilworth in a series of important papers [15, 16, 45–48] and also by Krull in [33]. Since that time, there has been substantial research regarding some specific classes of residuated structures, see for example [1, 9, 26] and [38], but we believe that this is the first time that a general structural theory has been established for the class ℛℒ as a whole. In particular, we develop the notion of a normal subalgebra and show that ℛℒ is an "ideal variety" in the sense that it is an equational class in which congruences correspond to "normal" subalgebras in the same way that ring congruences correspond to ring ideals. As an application of the general theory, we produce an equational basis for the important subvariety ℛℒC that is generated by all residuated chains. In the process, we find that this subclass has some remarkable structural properties that we believe could lead to some important decomposition theorems for its finite members (along the lines of the decompositions provided in [27]).

A new method for approximation of closed convex subsets of B(H)

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6005-6013
Author(s):  
Mahdi Iranmanesh ◽  
Fatemeh Soleimany
Keyword(s):  
Best Approximation ◽  
Numerical Range ◽  
New Method ◽  
C Algebra ◽  
Convex Subsets

In this paper we use the concept of numerical range to characterize best approximation points in closed convex subsets of B(H): Finally by using this method we give also a useful characterization of best approximation in closed convex subsets of a C*-algebra A.

scholarly journals The Poincaré half-space of a C$^*$-algebra

2019 ◽  
Vol 35 (7) ◽  
pp. 2187-2219
Author(s):  
Esteban Andruchow ◽  
Gustavo Corach ◽  
Lázaro Recht
Keyword(s):  
Half Space ◽  
C Algebra

scholarly journals Measuring Multijet Structure of Hadronic Energy Flow or, What is a jet?

1997 ◽  
Vol 12 (30) ◽  
pp. 5411-5529 ◽  
Author(s):  
Fyodor V. Tkachov
Keyword(s):  
Energy Flow ◽  
Mass Spectra ◽  
Analytical Control ◽  
Final States ◽  
C Algebra ◽  
Approximation Errors ◽  
Basic Class ◽  
Jet Algorithms ◽  
Hadronic Energy ◽  
Optimal Recombination

Ambiguities of jet algorithms are reinterpreted as instability wrt small variations of input. Optimal stability occurs for observables possessing property of calorimetric continuity (C-continuity) predetermined by kinematical structure of calorimetric detectors. The so-called C-correlators form a basic class of such observables and fit naturally into QFT framework, allowing systematic theoretical studies. A few rules generate other C-continuous observables. The resulting C-algebra correctly quantifies any feature of multijet structure such as the "number of jets" and mass spectra of "multijet substates." The new observables are physically equivalent to traditional ones but can be computed from final states bypassing jet algorithms which reemerge as a tool of approximate computation of C-observables from data with all ambiguities under analytical control and an optimal recombination criterion minimizing approximation errors.

scholarly journals Nuclear subalgebras of UHF C*-algebras

1986 ◽  
Vol 29 (1) ◽  
pp. 97-100 ◽  
Author(s):  
R. J. Archbold ◽  
Alexander Kumjian
Keyword(s):  
Tensor Product ◽  
Inductive Limit ◽  
Inductive Limits ◽  
C Algebra ◽  
C Algebras ◽  
Finite Dimensional ◽  
The Family ◽  
Algebraic Tensor Product

A C*-algebra A is said to be approximately finite dimensional (AF) if it is the inductive limit of a sequence of finite dimensional C*-algebras(see [2], [5]). It is said to be nuclear if, for each C*-algebra B, there is a unique C*-norm on the *-algebraic tensor product A ⊗B [11]. Since finite dimensional C*-algebras are nuclear, and inductive limits of nuclear C*-algebras are nuclear [16];,every AF C*-algebra is nuclear. The family of nuclear C*-algebras is a large and well-behaved class (see [12]). The AF C*-algebras for a particularly tractable sub-class which has been completely classified in terms of the invariant K0 [7], [5].

scholarly journals Note on amenable algebras of operators

1995 ◽  
Vol 52 (2) ◽  
pp. 327-329 ◽  
Author(s):  
P.C. Curtis ◽  
R.J. Loy
Keyword(s):  
C Algebra ◽  
Amenable Algebra ◽  
Algebra Of Operators

It is shown that an amenable algebra of operators on Hibert space which is generated by its normal elements is necessarily self-adjoint, so it is a C*-algebra.

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