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Isomorphisms of some reflexive algebras

Jiankui Li; Zhidong Pan — 2008

Studia Mathematica

Suppose ℒ₁ and ℒ₂ are subspace lattices on complex separable Banach spaces X and Y, respectively. We prove that under certain lattice-theoretic conditions every isomorphism from algℒ₁ to algℒ₂ is quasi-spatial; in particular, if a subspace lattice ℒ of a complex separable Banach space X contains a sequence $E_{i}$ such that $(E_{i}) ₋ \neq X$ , $E_{i} \subseteq E_{i + 1}$ , and $⋁_{i = 1}^{\infty} E_{i} = X$ then every automorphism of algℒ is quasi-spatial.

The Cayley transform of Banach algebras.

Pan, Zhidong — 2002

International Journal of Mathematics and Mathematical Sciences

A weak law of large numbers for the sample covariance matrix.

Sepanski, Steven J.; Pan, Zhidong — 2000

Electronic Communications in Probability [electronic only]

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Isomorphisms of some reflexive algebras

The Cayley transform of Banach algebras.

A weak law of large numbers for the sample covariance matrix.