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Extending Algebraic Operations to D-Completions

Klaus Keimel, Jimmie D. Lawson
2009 Electronical Notes in Theoretical Computer Science  
In this article we show how separately continuous 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.  ... 
doi:10.1016/j.entcs.2009.07.086 fatcat:b2pvji42czhcfdksnj5bytusmu

Extending algebraic operations to D-completions

Klaus Keimel, Jimmie D. Lawson
2012 Theoretical Computer Science  
and the laws that they satisfy, both identities and inequalities, can be 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.  ... 
doi:10.1016/j.tcs.2011.02.015 fatcat:iwyawhdqg5esdbtj2hqhurb2j4

Domain algebras [chapter]

Peter Dybjer
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?  ... 
doi:10.1007/3-540-13345-3_13 fatcat:e75yevtzw5a55pqaf4jqyccvmi

Covariant representations of subproduct systems

Ami Viselter
2010 Proceedings of the London Mathematical Society  
This paper is mainly concerned with finding conditions for a covariant representation of a subproduct system 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?  ... 
doi:10.1112/plms/pdq047 fatcat:4deokcupnrchze5lxyawo7iy7a

Free complete Wasserstein algebras [article]

Radu Mardare, Prakash Panangaden, Gordon D. Plotkin
2018 arXiv   pre-print
We present an 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.  ... 
arXiv:1802.07366v3 fatcat:a7jal652ojcuzcdqvefwyywsjq

Completely contractive projections on operator algebras

David Blecher, Matthew Neal
2016 Pacific Journal of Mathematics  
The main goal of this paper is 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.  ... 
doi:10.2140/pjm.2016.283.289 fatcat:s35r7mf5c5drpglfe4d3pbx7qe

Norming Algebras and Automatic Complete Boundedness of Isomorphisms of Operator Algebras

David R. Pitts
2006 arXiv   pre-print
that a bounded representation of a C*-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.  ... 
arXiv:math/0609604v1 fatcat:2dzqodoqgze4bmspib4jdzpmta

Extended-order algebras

Cosimo Guido, Paola Toto
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.  ... 
doi:10.1016/j.jal.2008.01.001 fatcat:4y42h7rscbcuhj43elqiuizozq

Extensions of operator algebras I

David P. Blecher, Maureen K. Royce
2008 Journal of Mathematical Analysis and Applications  
We transcribe a portion of the theory of extensions of C*-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.  ... 
doi:10.1016/j.jmaa.2007.07.065 fatcat:s2cmqx6pifhorggf3v6d56nqnq

Explicit construction of universal operator algebras and applications to polynomial factorization

David P. Blecher, Vern I. Paulsen
1991 Proceedings of the American Mathematical Society  
Using the characterization of unital 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.  ... 
doi:10.1090/s0002-9939-1991-1049839-7 fatcat:bv6rbwckibf33djown7ckcba6q

Explicit Construction of Universal Operator Algebras and Applications to Polynomial Factorization

David P. Blecher, Vern I. Paulsen
1991 Proceedings of the American Mathematical Society  
Using the characterization of unital 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.  ... 
doi:10.2307/2048708 fatcat:3lcqtwz2gfhz3altq5tatef2za

Norming algebras and automatic complete boundedness of isomorphisms of operator algebras

David R. Pitts
2007 Proceedings of the American Mathematical Society  
Secondly, we show that an isometric isomorphism between subalgebras A i of C * -diagonals (C i , 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  ... 
doi:10.1090/s0002-9939-07-09172-1 fatcat:7kscnimxjncevf3os3dzjwfitm

ON THE STRUCTURE OF ALMOST F-ALGEBRAS

Karim Boulabiar, Elmiloud Chil
2001 Demonstratio Mathematica  
This paper is mainly concerned with a representation theorem for almost /-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 .  ... 
doi:10.1515/dema-2001-0403 fatcat:d5qqthj3tvdybhklpjcx2j6iuu

Stone duality, topological algebra, and recognition [article]

Mai Gehrke
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.  ... 
arXiv:1309.2422v1 fatcat:olfwskljljev3b4g6bs7lofatm

Stone duality, topological algebra, and recognition

Mai Gehrke
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.  ... 
doi:10.1016/j.jpaa.2015.12.007 fatcat:kctw7epgojh3tpqrnfgfpi6d2e
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