Nonextreme de Branges-Rovnyak spaces as models for contractions

The de Branges--Rovnyak spaces are known to provide an alternate functional model for contractions on a Hilbert space, equivalent to the Sz.-Nagy--Foias model. The scalar de Branges--Rovnyak spaces $\mathcal{H}(b)$ have essentially different properties, according to whether the defining function $b$ is or not extreme in the unit ball of $H^\infty$. For $b$ extreme the model space is just $\mathcal{H}(b)$, while for $b$ nonextreme an additional construction is required. In the present paper we identify the precise class of contractions which have as a model $\mathcal{H}(b)$ with $b$ nonextreme.Comment: 15v page

Abstracts: Plenary Speakers

HI extensions of L ∞ spaces and spaces with very few operators Tuesday, July 30, HA4, We will present a general method of embedding Banach spaces with separable dual into L ∞ spaces admitting very few operators. In particular we will discuss the following two results. Theorem 1. (i) For every X with X * separable there exists a L ∞ space X such that X is isomorphic to a subspace X of X and X/ X is Hereditarily indecomposable satisfying the "scalar plus compact" property. (ii) If ℓ 1 is not isomorphic to a complemented subspace of X * then the aforementioned X satisfies the "scalar plus compact" property. The above yields that every separable reflexive space embeds into a L ∞ space satisfying the "scalar plus compact" property. ( HA4, It is well known that two non-isometric (and even non-isomorphic) Banach spaces can have isometric duals: the class of isometric preduals of l 1 provides classical examples. However, it frequently happens that a dual space has a unique isometric predual, as it is for instance the case for von Neumann algebras. We will provide simple topological tools which permit to show that weak-star closed spaces A of operators on a reflexive space X have unique isometric preduals as soon as weak-star approximation by compact operators is available in A. Some observations on approximation properties will also be mentioned. Pamela Gorkin (Bucknell University, USA) [email protected] Compositions of Blaschke products and three theorems of Frostman Thursday, August 1, HA4, 9:00-9:50 A recent Monthly article gave a very simple algorithm for determining when a polynomial is a composition of two (nontrivial) polynomials. A natural next step is to determine when finite Blaschke products are compositions of two Blaschke products, neither of which are automorphism of the disk. Well discuss several algorithms for determining when a finite Blaschke product can be a composition and then well discuss the current state of affairs for inner functions focusing, in particular, on three theorems of O. 2. M is in the closure of the set of injective factors on H with respect to the Effros-Marchal topology. 3. M admits an embedding i into the Ocneanu ultrapower N ω of the injective III 1 factor N with a normal faithful conditional expectation from N ω to M . 4. For every ε > 0, natural number n, and x 1 ,...,x n in natural cone P ♮ M in the standard form for M , there is a natural number k and a 1 , . . . , a n in . . , n, where tr k is the tracial state on M k (C). Magdalena Musat (University of Copenhagen, Denmark) [email protected] Factorizable completely positive maps and the Connes embedding problem Wednesday, July 31, HA4, The class of factorizable completely positive maps (originating in work of C. Anantharaman-Delaroche) has gained particular significance in quantum information theory in connection with the settling (in the negative) of the asymptotic quantum Birkhoff conjecture. More precisely, in joint work with Uffe Haagerup we proved earlier that every non-factorizable unital completely positive and trace-preserving map on M n (C), n ≥ 3, provides a counterexample for the conjecture. We will explain a recently established connection to the Connes embedding problem in terms of a newly formulated asymptotic property of factorizable maps. 3 Vern Paulsen (Houston University, USA) [email protected] Frames. Groups and the July 31, HA4, In this talk we will survey some of the new results on the Kadison-Singer problem and emphasize a few of the special cases that we believe are approachable. Volker Runde (University of Alberta, Canada) [email protected] Dual Banach algebras -an overview Sunday, August 4, HA4, A dual Banach algebra is a Banach algebra that is also a dual Banach space such that multiplication is separately weak* continuous. Von Neumann algebras are dual Banach algebras, but so are the measure algebras of locally compact groups. We discuss amenability properties for dual Banach algebras as well as their surprisingly intricate representation theory. Mikael Rørdam (University of Copenhagen, Denmark) [email protected] Supramenable groups and their actions on locally compact Hausdorff spaces Tuesday, July 30, HA4, It is well-known that a discrete group is amenable if and only if whenever it acts on a compact Hausdorff space, then there is an invariant probability measure. Similarly, a group is supramenable if and only if whenever it acts co-compactly on a locally compact Hausdorff space, then there is a nonzero invariant Radon measure. In this case the group admits a free minimal purely infinite (and often times also amenable) action on the locally compact (non-compact) Cantor set. We also discuss geometric characterizations of supramenable groups. The results are obtained by studying how groups act on their betacompactification. We shall discuss this action and its universal properties. This is joint work with J. Kellerhals and N. Monod, and in parts a work in progress with H. Matsui

Collected Papers (on various scientific topics), Volume XIII

This thirteenth volume of Collected Papers is an eclectic tome of 88 papers in various fields of sciences, such as astronomy, biology, calculus, economics, education and administration, game theory, geometry, graph theory, information fusion, decision making, instantaneous physics, quantum physics, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, scientific research methods, statistics, and others, structured in 17 chapters (Neutrosophic Theory and Applications; Neutrosophic Algebra; Fuzzy Soft Sets; Neutrosophic Sets; Hypersoft Sets; Neutrosophic Semigroups; Neutrosophic Graphs; Superhypergraphs; Plithogeny; Information Fusion; Statistics; Decision Making; Extenics; Instantaneous Physics; Paradoxism; Mathematica; Miscellanea), comprising 965 pages, published between 2005-2022 in different scientific journals, by the author alone or in collaboration with the following 110 co-authors (alphabetically ordered) from 26 countries: Abduallah Gamal, Sania Afzal, Firoz Ahmad, Muhammad Akram, Sheriful Alam, Ali Hamza, Ali H. M. Al-Obaidi, Madeleine Al-Tahan, Assia Bakali, Atiqe Ur Rahman, Sukanto Bhattacharya, Bilal Hadjadji, Robert N. Boyd, Willem K.M. Brauers, Umit Cali, Youcef Chibani, Victor Christianto, Chunxin Bo, Shyamal Dalapati, Mario Dalcín, Arup Kumar Das, Elham Davneshvar, Bijan Davvaz, Irfan Deli, Muhammet Deveci, Mamouni Dhar, R. Dhavaseelan, Balasubramanian Elavarasan, Sara Farooq, Haipeng Wang, Ugur Halden, Le Hoang Son, Hongnian Yu, Qays Hatem Imran, Mayas Ismail, Saeid Jafari, Jun Ye, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Abdullah Kargın, Vasilios N. Katsikis, Nour Eldeen M. Khalifa, Madad Khan, M. Khoshnevisan, Tapan Kumar Roy, Pinaki Majumdar, Sreepurna Malakar, Masoud Ghods, Minghao Hu, Mingming Chen, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohamed Loey, Mihnea Alexandru Moisescu, Muhammad Ihsan, Muhammad Saeed, Muhammad Shabir, Mumtaz Ali, Muzzamal Sitara, Nassim Abbas, Munazza Naz, Giorgio Nordo, Mani Parimala, Ion Pătrașcu, Gabrijela Popović, K. Porselvi, Surapati Pramanik, D. Preethi, Qiang Guo, Riad K. Al-Hamido, Zahra Rostami, Said Broumi, Saima Anis, Muzafer Saračević, Ganeshsree Selvachandran, Selvaraj Ganesan, Shammya Shananda Saha, Marayanagaraj Shanmugapriya, Songtao Shao, Sori Tjandrah Simbolon, Florentin Smarandache, Predrag S. Stanimirović, Dragiša Stanujkić, Raman Sundareswaran, Mehmet Șahin, Ovidiu-Ilie Șandru, Abdulkadir Șengür, Mohamed Talea, Ferhat Taș, Selçuk Topal, Alptekin Ulutaș, Ramalingam Udhayakumar, Yunita Umniyati, J. Vimala, Luige Vlădăreanu, Ştefan Vlăduţescu, Yaman Akbulut, Yanhui Guo, Yong Deng, You He, Young Bae Jun, Wangtao Yuan, Rong Xia, Xiaohong Zhang, Edmundas Kazimieras Zavadskas, Zayen Azzouz Omar, Xiaohong Zhang, Zhirou Ma.‬‬‬‬‬‬‬

Hypergroups with a strongly unilateral identity

Among hyperstructures of type U on the right having small size, the order 6 is a relevant case. Indeed, only if the order is \leq 6 there exist proper semihypergrops and hypergroups of type U on the right whose right scalar identity is not also left identity. In the present paper we show a construction of hypergroups of type U on the right whose right scalar identity is not also left identity. That construction characterizes completely the case of order 6, and allows to introduce a semi-ordering structure within that case. With the help of that semi-ordering, and of symbolic computation software, we show that these hypergroups can be obtained as hyperproduct extensions of 41 minimal hypergroups, and that the number of their isomorphism classes is 946