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Type and cotype of operator spaces

100%
Lee H.
Studia Mathematica
|
2008
|
tom 185
|
nr 3
219-247
EN
We consider two operator space versions of type and cotype, namely $S_{p}$-type, $S_{q}$-cotype and type (p,H), cotype (q,H) for a homogeneous Hilbertian operator space H and 1 ≤ p ≤ 2 ≤ q ≤ ∞, generalizing "OH-cotype 2" of G. Pisier. We compute type and cotype of some Hilbertian operator spaces and $L_{p}$ spaces, and we investigate the relationship between a homogeneous Hilbertian space H and operator spaces with cotype (2,H). As applications we consider operator space versions of generalized little Grothendieck's theorem and Maurey's extension theorem in terms of these new notions.
2
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Dimensions of components of tensor products of representations of linear groups with applications to Beurling-Fourier algebras

51%
Collins B., Lee H., Śniady P.
Studia Mathematica
|
2014
|
tom 220
|
nr 3
221-241
EN
We give universal upper bounds on the relative dimensions of isotypic components of a tensor product of representations of the linear group GL(n) and universal upper bounds on the relative dimensions of irreducible components of a tensor product of representations of the special linear group SL(n). This problem is motivated by harmonic analysis problems, and we give some applications to the theory of Beurling-Fourier algebras.
3
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Asymptotic spectral distributions of distance-k graphs of Cartesian product graphs

51%
Hibino Y., Lee H., Obata N.
Colloquium Mathematicum
|
2013
|
tom 132
|
nr 1
35-51
EN
Let G be a finite connected graph on two or more vertices, and $G^{[N,k]}$ the distance-k graph of the N-fold Cartesian power of G. For a fixed k ≥ 1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of $G^{[N,k]}$. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.
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