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Frobenius reciprocity and the Haagerup tensor product
2018
Transactions of the American Mathematical Society
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The characterisation, which builds on previous joint work with N. Higson, exhibits a close connection between the notions of adjoint operators and adjoint functors. ...
As an application, we prove a Frobenius reciprocity theorem for representations of locally compact groups on operator spaces: the functor of unitary induction for a closed subgroup H of a locally compact ...
In [CH16] we showed that the natural extension of Ind G P to a functor on operator modules possesses a left adjoint. ...
doi:10.1090/tran/7203
fatcat:uaud5ylh3zawrghdh326tjkg44
Frobenius reciprocity and the Haagerup tensor product
[article]
2017
arXiv
pre-print
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2016 pre-print arXiv:1605.06023v1 fatcat:zh7flyp3mvh4pm6dx453cgq3q4
The characterisation, which builds on previous joint work with N. Higson, exhibits a close connection between the notions of adjoint operators and adjoint functors. ...
As an application, we prove a Frobenius reciprocity theorem for representations of locally compact groups on operator spaces: the functor of unitary induction for a closed subgroup H of a locally compact ...
By definition, a functor : OM(B) → OM(A) is strongly continuous if the maps : CB B (X , Y ) → CB A ( X , Y ) are strong-operator continuous on bounded subsets. ...
arXiv:1605.06023v2
fatcat:msg2vr5bcnh3nje5dtkh47egum
Measurable Categories
[article]
2004
arXiv
pre-print
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We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of bounded operators. ...
Several important technical results are established along the way: First it is shown that all bounded invertible additive functors (and thus a fortiori all invertible *-functors) between categories of ...
bounded fields of operators on X. ...
arXiv:math/0309185v2
fatcat:hezyftn6snfonlm5gud4ft3mt4
Page 4443 of Mathematical Reviews Vol. 58, Issue 6
[page]
1979
Mathematical Reviews
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The principal result here is that there is a one-to-one correspondence between subfunctors of B” and pre-Banach left ideals in B(H), the space of bounded linear operators on H, while the Banach left ideals ...
The paper deals with a special type of bounded linear operators mapping the space of bounded linear operators L(F,G) into the space L(E,H), where E, F, G and H are Banach spaces. ...
K-Theory of Stable Generalized Operator Algebras
2002
K-theory
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It is proved that algebraic and topological K-functors are isomorphic on the category of stable generalized operator algebras which are K i -regular for all i > 0. 2000 Mathematics Subject Classification ...
Namely it is proved the equality of algebraic and topological K-functors on the category of stable generalized operator algebras (Theorems 9 and 11). ...
Composing f with the canonical bounded homomorphism B → B α for each C * -seminorm α on B one gets ||f (a)|| α ≤ ||a|| for any a ∈ A. ...
doi:10.1023/a:1021197520756
fatcat:yqh37mns25a75mcgbvx4wzowyy
Pseudo effect algebras as algebras over bounded posets
[article]
2019
arXiv
pre-print
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2019 pre-print arXiv:1903.05399v1 fatcat:j2ydw3eshfgftgiomcdibzkyju
We prove that there is a monadic adjunction between the category of bounded posets and the category of pseudo effect algebras. ...
Let us focus on the partial operation / -or, as explained in the previous paragraph, a natural transformation /. ...
Actually, we equipped the bounded poset Q with a partial binary operation /, that is defined for all comparable pairs of elements of Q. In an analogous way, we may define a partial operation \ on Q. ...
arXiv:1903.05399v2
fatcat:gwoduvpdszcgbndfydtsrmnpwq
Infinite-Dimensionality in Quantum Foundations: W*-algebras as Presheaves over Matrix Algebras
2017
Electronic Proceedings in Theoretical Computer Science
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In short, complete boundedness is not formalizable in terms of topology. In detail, an abstract operator space is a compatible choice of norms on E, M 2 (E), M 3 (E), · · · for a Banach space E. ...
A (concrete) operator space is a closed subspace of a C*-algebra, or alternatively a Banach space given together with an isometric embedding into the space of all bounded operators on some Hilbert space ...
Considering that the composite of two full and faithful functors is full and faithful, one obtains the following corollary. Corollary 1. The functor NPLF is full and faithful. ...
doi:10.4204/eptcs.236.11
fatcat:qic6uywssrfsbft7jauhkeuobq
Expressivity of coalgebraic modal logic: The limits and beyond
2008
Theoretical Computer Science
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We then move on to polyadic modal logic, where modal operators may take more than one argument formula. We show that every accessible functor admits an expressive polyadic modal logic. ...
Expressivity results stating that, conversely, logically indistinguishable states are behaviourally equivalent depend on the existence of separating sets of predicate liftings for the signature functor ...
Acknowledgements The author wishes to thank Till Mossakowski, Markus Roggenbach, and Horst Reichel for collaboration on COCASL, Erwin R. ...
doi:10.1016/j.tcs.2007.09.023
fatcat:yaqkhmwfyrcljagjcvqrthvgde
ADJOINT FUNCTORS BETWEEN CATEGORIES OF HILBERT -MODULES
2016
Journal of the Institute of Mathematics of Jussieu
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In this way we shall show that the parabolic induction functor has a simultaneous left and right adjoint, namely the parabolic restriction functor constructed in Clare et al. ...
The purpose of this paper is to study adjunctions between functors of this sort. ...
Being a bounded operator between Hilbert spaces, δ X has an adjoint operator (3.20) η X : X −→ F ⊗ B F * ⊗ A X, and we obtain a natural transformation from the identity functor on A H to the tensor product ...
doi:10.1017/s1474748016000074
fatcat:2utpmxewrvb5bcjj46lm7dum7u
Expressivity of Coalgebraic Modal Logic: The Limits and Beyond
[chapter]
2005
Lecture Notes in Computer Science
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We then move on to polyadic modal logic, where modal operators may take more than one argument formula. We show that every accessible functor admits an expressive polyadic modal logic. ...
Expressivity results stating that, conversely, logically indistinguishable states are behaviourally equivalent depend on the existence of separating sets of predicate liftings for the signature functor ...
Acknowledgements The author wishes to thank Till Mossakowski, Markus Roggenbach, and Horst Reichel for collaboration on CoCasl, Erwin R. ...
doi:10.1007/978-3-540-31982-5_28
fatcat:7azakd6xmvbn7h5rcv4ycu67sy
Page 652 of Mathematical Reviews Vol. 49, Issue 2
[page]
1975
Mathematical Reviews
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Our goal is to describe the structure of the functors between these categories. For functors 6: BW and F: W->B there are defined natural transformations 7:6—>F and %: F—>6, the Banach space n.t. ...
OPERATOR THEORY
Let T be a bounded linear operator in Hilbert space, W(T)={(Tx, x): ||a|| =1} its numerical range. The author
reproves a theorem of 8. Hildebrandt [Math. ...
Measurable Categories and 2-Groups
[article]
2003
arXiv
pre-print
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bounded fields of bounded operators on X. ...
A measurable field of bounded operators is bounded if x → φ x x is a bounded real-valued function (Here x denotes the operator norm on B(H x , K x ).) ...
arXiv:math/0305176v1
fatcat:nfm7a6jbcvhldgjduwu6objvvi
A Categorical Setting for Lower Complexity
2010
Electronical Notes in Theoretical Computer Science
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Polarized operators A polarized operator F on an X-strong category consists of a pair of strong functors F p : Y n − → Y, and F o : X n − → X, and a map of cross maps F op : (X 1 , 1) f 1 − − → Y 1 · · ...
Polarized operators compose as operations on a polarized strong category. Thus, further examples can be generated from the above basic examples. ...
doi:10.1016/j.entcs.2010.08.017
fatcat:e3wsd2dxvnfz7bukgmiznkvd3m
Page 7137 of Mathematical Reviews Vol. , Issue 2002J
[page]
2002
Mathematical Reviews
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Then a Janus functor from Q to abelian groups is two functors M, and M”*, one covariant and one contravariant, which have the same value on objects. ...
The (Kock-Zoberlein) monad of bounded ideals on the category of orders is studied and an order admitting bounded suprema satisfies the above-mentioned infinite distributive law if the map sending a bounded ...
C∗-categories, groupoid actions, equivariant KK-theory, and the Baum–Connes conjecture
2004
Journal of Functional Analysis
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The operator T is called the adjoint of the operator T . An operator T is called bounded if the norm T = sup{ T A | A ∈ Ob(B)} is finite. The adjoint of a bounded operator is bounded. ...
It is shown in [19] that an operator T : E → F is a natural transformation, each map T A : E(A) → F(A) is bounded and linear, and the collection of maps T A defines an operator T . ...
Then by proposition 6.10, and naturality of the Kasparov product and descent map, we have a commutative diagram Taking direct limits, the desired result follows. ...
doi:10.1016/j.jfa.2004.04.016
fatcat:ignx3qrxrfex3h36miz7m4hkjq
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