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Florin Radulescu

Publications and source records attributed to Florin Radulescu.

24 records · Page 2Linked to original sources
arXiv2002

A comparison between the max and min norms on $C^*(F_n) \otimes C^*(F_n)$

Let $F_n$, $n\geq2$, be the free group with $n$ generators, denoted by $U_1,U_2,...,U_n$. Let $C*(F_n)$ be the full $C^*$-algebra of $F_n$. Let $\mathcal{X}$ be the vector subspace of the algebraic tensor product $C^*(F_n) \otimes C^*(F_n)$, spanned by $1\otimes1,U_1\otimes1,...,U_n\otimes1,1\otimes U_1,...,1\otimes U_n$. Let $|| \cdot ||_{\min}$ and $|| \cdot ||_{\max}$ be the minimal and maximal $C^*$ tensor norms on $C^*(F_n) \otimes C^*(F_n)$, and use the same notation for the corresponding (matrix) norms induced on $M_k(\mathbb{C})\otimes\mathcal{X}$. Identifying $\mathcal{X}$ with the subspace of $C^*(F_{2n})$ obtained by mapping $U_1\otimes1,...,1\otimes U_n$ into the $2n$ generators and the identity into the identity, we get a matrix norm $|| \cdot ||_{C^*(F_{2n})}$ which dominates the $|| \cdot ||_{\max}$ norm, on $M_k(\mathbb{C})\otimes\mathcal{X}$. In this paper we prove that, with $N=2n+1=\dim\mathcal{X}$, we have $||X||_{\max} \leq ||X||_{C^*(F_{2n})} \leq (N^2-N)^{1/2} ||X||_{\min}, X\in M_k(\mathbb{C})\otimes\mathcal{X}$.

math.OA↗
arXiv2001

Rescalings of free products of II_1 factors

We introduce notation Q(1) * ... * Q(n) * L(F_r)$ for von Neumann algebra II_1 factors where $r$ is allowed to be negative. This notation is defined by rescalings of free products of II_1 factors, and is proved to be consistent with known results and natural operations. We also give two statements which we prove are equivalent to isomorphism of free group factors.

math.OA↗
arXiv2000

Compressions of free products of von Neumann algebras

A reduction formula for compressions of von Neumann algebras arising as free products is proved. This shows that the fundamental group is all of the positive reals for some such algebras. Additionally, by taking a sort of free product with an unbounded semicircular element, continuous one parameter groups of trace scaling automorphisms on II_infinity factors are constructed; this produces type III_1 factors with core M tensor B(H), where M can be a full II_1-factor without the Haagerup approximation property.

math.OA↗
arXiv1999

Index of $Γ$-equivariant Toeplitz operators

Let $Γ$ be a discrete icc subgroup of PSL(2,R) of infinite covolume. and let M denote the quotient of the unit disc by $Γ$. We prove that a Toeplitz operator with $Γ$-invariant symbol f in C(M) is Brauer Fredholm if its symbol is invertible on the boundary of M and its Brauer index is equal to the winding number of f at the boundary. We construct the associated extension of the algebra of functions continuous on the boundary of M by the Brauer ideal in the C*-algebra generated by such operators.

math.OA↗
arXiv1995

Some estimates for the Banach space norms in the von Neumann algebras associated with the Berezin's quantization of compact Riemann

Let $\G$ be any cocompact, discrete subgroup of $\pslr$. In this paper we find estimates for the predual and the uniform Banach space norms in the von Neumann algebras associated with the Berezin' s quantization of a compact Riemann surface $\Bbb D/\G$. As a corollary, for large values of the deformation parameter $1/h$, these von Neumann algebras are isomorphic. Using the results in [AS], [AC], [GHJ] on the von Neumann dimension of the Hilbert spaces in the discrete series of unitary representations of $PSL(2,\Bbb R)$, as left modules over $Γ$ we deduce that the fundamental group ([MvN]) of the von Neumann $\Cal L(Γ)$ contains the positive rational numbers. Equivalently, this proves that the algebras $\Cal L(Γ)\otimes M_n(\Bbb C)$, are isomorphic for all $n$.

funct-an↗
arXiv1995

On the $Γ$-equivariant form of the Berezin's quantization of the upper half plane

Let $Γ$ be a fuchsian subgroup of \pslr. In this paper we consider the $Γ$-equivariant form of the Berezin's quantization of the upper half plane which will correspond to a deformation quantization of the (singular) space $\Bbb H/Γ$. Our main result is that the von Neumann algebra associated to the $Γ-$ equivariant form of the quantization is stable isomorphic with the von Neumann algebra associated to $Γ$.

funct-an↗