Alvaro Arias
In this paper we prove that several operator algebras are completely isomorphic to each other; e.g., the $C^*_λ(F_k)$, $k\geq 2$, the $C^*$-algebras generated by the regular left representation $λ:F_k\to B(\ell_2(F_k))$, are completely isomorphic to each other. We also study the ``non-commutative'' analytic spaces introduced by G. Popescu [Po], and give applications to Popescu's version of Von Neumann's inequality.
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Let $G$ be a locally compact group and $ω$ be a continuous weight on $G$. In this paper, we first characterize bicontinuous biseparating algebra isomorphisms between weighted $L^p$-algebras. As a result we extend previous results of Edwards, Strichartz and Parrot on algebra isomorphisms between $L^p$-algebras to the setting of weighted $L^p$-algebras. We then study the automorphisms of certain weighted $L^p$-algebras on integers, applying known results on composition operators on classical function spaces.
We consider gerenalizated permutation equivalence of Vielenkin system on commutative compact torsion finite exponent groups.
Isometric Jordan isomorphisms of group algebras
本文证明局部紧群代数之间的收缩 Jordan 同构必为等距同构或等距反同构，并借此研究群代数上的等距双边零积保持映射及局部等距自同构。
Classical Segal-Bargmann theory studies three Hilbert space unitary isomorphisms that describe the wave-particle duality and the configuration space-phase space. In this work, we generalized these concepts to Clifford algebra-valued functions. We establish the unitary isomorphisms among the space of Clifford algebra-valued square-integrable functions on $\mathbb{R}^n$ with respect to a Gaussian measure, the space of monogenic square-integrable functions on $\mathbb{R}^{n+1}$ with respect to another Gaussian measure and the space of Clifford algebra-valued linear functionals on symmetric tensor…
Let $Ω$ denote an algebra of sets and $μ$ a $σ$-finite measure. We then prove that the completion of $Ω$ under the pseudometric $d(A,B)$ = $μ^{\ast}(A \triangle B)$ is $σ$-algebra isomorphic and isometric to the Caratheodory Extension of $Ω$ under the equivalence relation $\sim$.
In this article we observe that a locally compact group $G$ is completely determined by the algebraic properties of its Feichtinger's Segal algebra $S_0(G).$ Let $G$ and $H$ be locally compact groups. Then any linear (not necessarily continuous) bijection of $S_0(G)$ onto $S_0(H)$ which preserves the convolution and pointwise products is essentially a composition with a homeomorphic isomorphism of $H$ onto $G.$
About an isomorphism between the Beurling algebra with a weight dependent convolution and the $L^1(G)$ group algebra
本文证明带权依赖卷积的 Beurling 代数与群代数$L^1(G)$同构，并借此推广已有结果，建立群酉表示与该代数非退化$\ast$-表示的等价。
Isomorphisms of Tits--Kantor--Koecher Lie algebras of JB*-triples
本文将 JB*-三元组的 Tits--Kantor--Koecher 李代数同构刻画为满射线性等距，证明其范畴等价性，并引入三元幂等概念，证明特定序同构可延拓为实线性同构。
We investigate the lifting property of modulation spaces and construct explicit isomorpisms between them. For each weight function $ω$ and suitable window function $\fy $, the Toeplitz operator (or localization operator) $\tp_\fy (ω)$ is an isomorphism from $M^{p,q}_{(ω_0)}$ onto $M^{p,q}_{(ω_0/ω)}$ for every $p,q \in [1,\infty ]$ and arbitrary weight function $ω_0$. The methods involve the pseudo-differential calculus of Bony and Chemin and the Wiener algebra property of certain symbol classes of pseudo-differential operators.
Order isomorphisms on positive cones of non-unital $C^*$-algebras
本文研究非单位 $C^*$-代数正锥上的正齐次序同构，证明其可加性并延拓为自伴部分间的有界实线性同构，进而给出表示定理，并推广了保持算术平均范数的满射映射的先前结果。
We study the family of isomorphisms and strictly singular operators in mixed Tsirelson spaces and their modified versions setting. We show sequential minimality of modified mixed Tsirelson spaces $T_M[(\mc{S}_n,θ_n)]$ satisfying some regularity conditions and present results on existence of strictly singular non-compact operators on subspaces of mixed Tsirelson spaces defined by the families $(\mc{A}_n)_n$ and $(\mc{S}_n)_n$.
Following a result of Hatori, Miura and Tagaki ([4]) we give here a spectral characterization of an isomorphism from a $C^\star$-algebra onto a Banach algebra. We then use this result to show that a $C^\star$-algebra $A$ is isomorphic to a Banach algebra $B$ if and only if there exists a surjective function $ϕ:A\rightarrow B$ satisfying (i) $σ\left(ϕ(x)ϕ(y)ϕ(z)\right)=σ\left(xyz\right)$ for all $x,y,z\in A$ (where $σ$ denotes the spectrum), and (ii) $ϕ$ is continuous at $\mathbf 1$. A simple example shows that (i) cannot be relaxed to products of two elements, as is the case with commutative B…
The inter-relationship between isomorphisms of commutative and isomorphisms of non-commutative $\log$-algebras
本文研究了非交换 $\log$-代数的同构问题，建立了由不同精确正规半有限迹构造的非交换 $\log$-代数重合及同构的充分必要条件，并揭示了其与 von Neumann 代数中心上 $\log$-代数同构的联系。
Generalizing von Neumann's result on type II$_1$ von Neumann algebras, we characterize lattice isomorphisms between projection lattices of arbitrary von Neumann algebras by means of ring isomorphisms between the algebras of locally measurable operators. Moreover, we give a complete description of ring isomorphisms of locally measurable operator algebras when the von Neumann algebras are without type II direct summands.
Order isomorphisms in $C^*$-algebras
本文研究了$C^*$-代数中自共轭部分和$AW^*$-代数中一般算子区间之间的序同构，利用Jordan $^*$-同构和闭算子进行描述，扩展了冯·诺依曼代数的相关结果。
In this paper a full description of order isomorphisms between effect algebras of atomic JBW-algebras is given. We will derive a closed formula for the order isomorphisms on the effect algebra of type I factors by proving that the invertible part of the effect algebra of a type I factor is left invariant. This yields an order isomorphism on the whole cone, for which a characterisation exists. Furthermore, we will show that the obtained formula for the order isomorphism on the invertible part can be extended to the whole effect algebra again. As atomic JBW-algebras are direct sums of type I fac…
We prove that algebraic isomorphisms between limit algebras are automatically continuous, and consider consequences of this result. In particular, we give partial solutions to a conjecture of Power [Limit Algebras, Longman, 1992, Notes to Chapter 8] and to an open problem [op. cit., Problem 7.8]. As a further consequence, we describe epimorphisms between various classes of limit algebras.
We show that for any smooth Hausdorff manifolds M and N, which are not necessarily second countable, paracompact or connected, any isomorphism from the algebra of smooth (real or complex) functions on N to the algebra of smooth functions on M is given by composition with a unique diffeomorphism from M to N. An analogous result holds true for isomorphisms of algebras of smooth functions with compact support.
In this paper we completely describe the order isomorphisms between cones of atomic JBW-algebras. Moreover, we can write an atomic JBW-algebra as an algebraic direct summand of the so-called engaged and disengaged part. On the cone of the engaged part every order isomorphism is linear and the disengaged part consists only of copies of $\mathbb{R}$. Furthermore, in the setting of general JB-algebras we prove the following. If either algebra does not contain an ideal of codimension one, then every order isomorphism between their cones is linear if and only if it extends to a homeomorphism, betwe…
We continue the study of isomorphisms of tensor algebras associated to a C*-correspondences in the sense of Muhly and Solel. Inspired by by recent work of Davidson, Ramsey and Shalit, we solve isomorphism problems for tensor algebras arising from weighted partial dynamical systems. We provide complete bounded / isometric classification results for tensor algebras arising from weighted partial systems, both in terms of the C*-correspondences associated to them, and in terms of the original dynamics. We use this to show that the isometric isomorphism and algebraic / bounded isomorphism problems …
This article presents an isomorphism between two operator algebras $L_1$ and $L_2$ where $L_1$ is the set of operators on a space of Hilbert-Schmidt operators and $L_2$ is the set of operators on a tensor product space. We next compare our isomorphism to a well-known result called Choi's isomorphism theorem. The advantage of Choi's isomorphism is that it takes completely positive maps to positive operators. One advantage of our isomorphism is that it applies to infinite dimensional Hilbert spaces, while Choi's isomorphism only holds for finite dimensions. Also, our isomorphism preserves operat…
Isomorphisms of Birkhoff-James orthogonality on finite-dimensional $C^*$-algebra
该研究对有限维复$C^*$-代数上强保持Birkhoff-James正交性的双射映射分类，发现其接近实线性等距映射且结构可确定，解决了相关映射的结构刻画问题。
We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X. We also identify the multiplicative linear functionals from the special algebra of Colombeau generalized functions on X to the ring of Colombeau generalized numbers. Up to multiplication with an idempotent generalized number, they are given by an evaluation map at a compactly supported generalized point on X.
We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maximal algebras of truncated Toeplitz operators.
We discuss an extension of Toeplitz quantization based on polyanalytic functions. We derive isomorphism theorem for polyanalytic Toeplitz operators between weighted Sobolev-Fock spaces of polyanalytic functions, which are images of modulation spaces under polyanalytic Bargmann transforms. This generalizes well-known results from the analytic setting. Finally, we derive an asymptotic symbol calculus and present an asymptotic expansion of complex Weyl operators in terms of polyanalytic Toeplitz operators.
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