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Extending Algebraic Operations to D-Completions

2009
*
Electronical Notes in Theoretical Computer Science
*

In this article we show how separately continuous

doi:10.1016/j.entcs.2009.07.086
fatcat:b2pvji42czhcfdksnj5bytusmu
*algebraic**operations*on T 0 -spaces and the laws that they satisfy, both identities and inequalities, can be*extended**to*the*D*-*completion*, that is, the ... Indeed we show that the*operations*can be*extended**to*the lattice of closed sets, but in this case it is only the linear identities that admit extension. ... Acknowledgement The authors wish*to*acknowledge and thank Achim Jung for helpful discussions and insights in the preparation of this paper. ...##
###
Extending algebraic operations to D-completions

2012
*
Theoretical Computer Science
*

and the laws that they satisfy, both identities and inequalities, can be

doi:10.1016/j.tcs.2011.02.015
fatcat:iwyawhdqg5esdbtj2hqhurb2j4
*extended**to*the*D*-*completion*, that is, the universal monotone convergence space*completion*. ... Extension of*algebraic**operations*Extension of identities dcpo-*completion*Free*algebra*constructions a b s t r a c t In this article, we show how separately continuous*algebraic**operations*on T 0 -spaces ... Acknowledgements The authors wish*to*acknowledge and thank Achim Jung for helpful discussions and insights in the preparation of this paper. ...##
###
Domain algebras
[chapter]

1984
*
Lecture Notes in Computer Science
*

*D*. Lawson.

*Extending*

*algebraic*

*operations*

*to*

*D*-

*completions*. In S. Abramsky, M. Mislove, and C. ... The (

*extended*)

*algebraic*

*operations*on Γ can be restricted

*to*P .

*Completing*semitopological

*algebras*-second attempt Theorem. ... The

*D*-

*completion*, the sobrification, and the round ideal

*completion*of a C-space all coincide. Is there a simple argument that shows that free

*algebras*exist for C-spaces? ...

##
###
Covariant representations of subproduct systems

2010
*
Proceedings of the London Mathematical Society
*

This paper is mainly concerned with finding conditions for a covariant representation of a subproduct system

doi:10.1112/plms/pdq047
fatcat:4deokcupnrchze5lxyawo7iy7a
*to**extend**to*a C^*-representation of the Toeplitz*algebra*. ... A celebrated theorem of Pimsner states that a covariant representation T of a C^*-correspondence E*extends**to*a C^*-representation of the Toeplitz*algebra*of E if and only if T is isometric. ... When does a (*completely*contractive) covariant representation*extend**to*a C * -representation? ...##
###
Free complete Wasserstein algebras
[article]

2018
*
arXiv
*
pre-print

We present an

arXiv:1802.07366v3
fatcat:a7jal652ojcuzcdqvefwyywsjq
*algebraic*account of the Wasserstein distances W_p on*complete*metric spaces, for p ≥ 1. ... In particular, we give axioms, parametric in p, for*algebras*over metric spaces equipped with probabilistic choice*operations*. ... It suffices*to*show that every*complete*Wasserstein midpoint*algebra*of order p can be*extended**to**complete*Wasserstein barycentric*algebra*of order p with the same carrier. Let A be such an*algebra*. ...##
###
Completely contractive projections on operator algebras

2016
*
Pacific Journal of Mathematics
*

The main goal of this paper is

doi:10.2140/pjm.2016.283.289
fatcat:s35r7mf5c5drpglfe4d3pbx7qe
*to*find*operator**algebra*variants of certain deep results of Stormer, Friedman and Russo, Choi and Effros, Effros and Stormer, Robertson and Youngson, Youngson, and others ... In particular we investigate the 'bicontractive projection problem' and related questions in the category of*operator**algebras*. ... Some of this material was presented at the AMS Special Session on*Operator**Algebras*and Their Applications: A Tribute*to*Richard V. ...##
###
Norming Algebras and Automatic Complete Boundedness of Isomorphisms of Operator Algebras

2006
*
arXiv
*
pre-print

that a bounded representation of a C*-

arXiv:math/0609604v1
fatcat:2dzqodoqgze4bmspib4jdzpmta
*algebra*is similar*to*a *-representation precisely when the image*operator**algebra*\lambda-norms itself. ... We combine the notion of norming*algebra*introduced by Pop, Sinclair and Smith with a result of Pisier*to*show that if A_1 and A_2 are*operator**algebras*, then any bounded epimorphism of A_1 onto A_2 is ... Acknowledgment: This work was*completed*during a visit*to*the University of Waterloo. ...##
###
Extended-order algebras

2008
*
Journal of Applied Logic
*

*Extended*-order

*algebras*are defined, whose

*operation*

*extends*the order relation of a poset with a greatest element. ... Several classes of

*extended*-order

*algebras*are considered that lead

*to*most well known multiplicative ordered structures by means of adjunction, once the

*completion*process due

*to*MacNeille is applied. ...

*to*embed (some kind of)

*extended*-order

*algebras*into

*complete*extensions. ...

##
###
Extensions of operator algebras I

2008
*
Journal of Mathematical Analysis and Applications
*

We transcribe a portion of the theory of extensions of C*-

doi:10.1016/j.jmaa.2007.07.065
fatcat:s2cmqx6pifhorggf3v6d56nqnq
*algebras**to*general*operator**algebras*. ... We also include several new general facts about approximately unital ideals in*operator**algebras*and the C*-*algebras*which they generate. ... The former, C * max (B), is characterized by its universal property: every*completely*contractive homomorphism π : B →*D*into a C * -*algebra**D**extends**to*a * -homomorphism C * max (B) →*D*. ...##
###
Explicit construction of universal operator algebras and applications to polynomial factorization

1991
*
Proceedings of the American Mathematical Society
*

Using the characterization of unital

doi:10.1090/s0002-9939-1991-1049839-7
fatcat:bv6rbwckibf33djown7ckcba6q
*operator**algebras*developed in [6], we give explicit internal definitions of the free product and the maximal*operator*-*algebra*tensor product of*operator**algebras*and ... This approach leads*to*new factorization theorems for polynomials in one and two variables. ...*algebra*A(*D*x*D*),*completely*isometrically. ...##
###
Explicit Construction of Universal Operator Algebras and Applications to Polynomial Factorization

1991
*
Proceedings of the American Mathematical Society
*

Using the characterization of unital

doi:10.2307/2048708
fatcat:3lcqtwz2gfhz3altq5tatef2za
*operator**algebras*developed in [6], we give explicit internal definitions of the free product and the maximal*operator*-*algebra*tensor product of*operator**algebras*and ... This approach leads*to*new factorization theorems for polynomials in one and two variables. ...*algebra*A(*D*x*D*),*completely*isometrically. ...##
###
Norming algebras and automatic complete boundedness of isomorphisms of operator algebras

2007
*
Proceedings of the American Mathematical Society
*

Secondly, we show that an isometric isomorphism between subalgebras A i of C * -diagonals (C i ,

doi:10.1090/s0002-9939-07-09172-1
fatcat:7kscnimxjncevf3os3dzjwfitm
*D*i ) (i = 1, 2) satisfying*D*i ⊆ A i ⊆ C i*extends*uniquely*to*a * -isomorphism of the C * -*algebras*generated ... The purpose of this note is*to*give a sufficient condition on an*operator**algebra*B which ensures that every bounded epimorphism u : A → B of the*operator**algebra*A onto B is*completely*bounded. ... License or copyright restrictions may apply*to*redistribution; see https://www.ams.org/journal-terms-of-use NORMING*ALGEBRAS*AND AUTOMATIC*COMPLETE*BOUNDEDNESS ...##
###
ON THE STRUCTURE OF ALMOST F-ALGEBRAS

2001
*
Demonstratio Mathematica
*

This paper is mainly concerned with a representation theorem for almost /-

doi:10.1515/dema-2001-0403
fatcat:d5qqthj3tvdybhklpjcx2j6iuu
*algebras*. ... in the Dedekind*completion*A 6 of A,*extending*the multiplication in A, such that A 6 is an almost /-*algebra*(respectively, a*d*-*algebra*) with respect*to*this*extended*multiplication. ... According*to*the Kantorovic theorem [1, Theorem 2.8], T*extends**to*a positive*operator*T from a (A 6 ) p into A 6 . ...##
###
Stone duality, topological algebra, and recognition
[article]

2013
*
arXiv
*
pre-print

*to*profinite

*completion*in mathematics in general. ... Our main result is that any topological

*algebra*based on a Boolean space is the

*extended*Stone dual space of a certain associated Boolean

*algebra*with additional

*operations*. ... The profinite

*completion*A is homeomorphic as a topological

*algebra*

*to*the

*extended*Stone dual of Rec(A), the Boolean

*algebra*with residuation

*operations*of recognizable subsets of A. ...

##
###
Stone duality, topological algebra, and recognition

2016
*
Journal of Pure and Applied Algebra
*

*to*profinite

*completion*in mathematics in general. ... Our main result is that any topological

*algebra*based on a Boolean space is the

*extended*Stone dual space of a certain associated Boolean

*algebra*with additional

*operations*. ... The profinite

*completion*A is homeomorphic as a topological

*algebra*

*to*the

*extended*Stone dual of Rec(A), the Boolean

*algebra*with residuation

*operations*of recognizable subsets of A. ...

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