Finite-Dimensional Subspaces of the p-Adic Space ℓ∞

Finite dimensional subspaces of

We discuss the nite dimensional structure theory of L p ; in particular, the theory of restricted invertibility and classiication of subspaces of`n p .

p-adic unit roots of L-functions over finite fields

In this brief note, we consider p-adic unit roots or poles of L-functions of exponential sums defined over finite fields. In particular, we look at the number of unit roots or poles, and a congruence relation on the units. This raises a question in arithmetic mirror symmetry.

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES

Hyperreflexivity of Finite-dimensional Subspaces

We show that each reflexive finite-dimensional subspace of operators is hyperreflexive. This gives a positive answer to a problem of Kraus and Larson. We also show that each n– dimensional subspace of Hilbert space operators is [ √ 2n]–hyperreflexive.

Finite dimensional subspaces of Lp

We discuss the finite dimensional structure theory of L p ; in particular, the theory of restricted invertibility and classification of subspaces of ℓ n p .