Let S(0,1) be the *-algebra of all classes Lebesgue measurable functions on unit interval (0,1) and let a complete symmetric Δ-normed *-subalgebra S(0,1), in which simple are dense, e.g., L∞(0,1), Llog(0,1), Arens algebra Lω(0,1) equipped with their natural Δ-norms. We show that there exists no non-trivial derivation commuting dyadic translations interval. type II (or I∞) von Neumann algebra, a...

We find estimates on the norms commutators of the form [f(x), y] in terms of the norm of [x, y], assuming that x and y are contactions in a C*-algebra A, with x normal and with spectrum within the domain of f . In particular we discuss ‖[x, y]‖ and ‖[x, y]‖ for 0 ≤ x ≤ 1. For larger values of δ = ‖[x, y]‖ we can rigorous calculate the best possible upper bound ‖[f(x), y]‖ ≤ ηf (δ) for many f . ...

1. Concerning These Notes 2 2. Introduction (First Day) 2 3. Algebraic Numbers and Integers 5 4. Linear Algebra for Number Theory 10 5. Review of Field Theory; Traces/Norms 10 6. Units: Some Notes Missing Here 16 7. Diophantine Approximation 16 8. The Trace Pairing 18 9. Linear Algebra and Discriminants 21 10. The Ring of Integers Inside the Number Field 26 11. Some Computational Aspects of Dis...

Let R be a perfect Fp-algebra, equipped with the trivial norm. Let W (R) be the ring of p-typical Witt vectors over R, equipped with the p-adic norms. We prove that via the Teichmüller map, the nonarchimedean analytic space (in the sense of Berkovich) associated to R is a (strong) deformation retract of the space associated to W (R).

Using a technique based on the Yangian Gelfand-Zetlin algebra and the associated Yangian Gelfand-Zetlin bases we construct an orthogonal basis of eigenvectors in the Calogero-Sutherland Model with spin, and derive product-type formulas for norms of these eigenvectors. 1 e-mail: [email protected] 2 e-mail: [email protected]

Using generalized Caputo fractional left and right vectorial Taylor formulae, we establish mixed Ostrowski Grüss type inequalities involving several Banach algebra valued functions. The estimates are with respect to all norms ∥·∥p, 1 ≤p ≤∞.

We study noncommutative C∗-algebras arising in geometric topology. Our object are Thurston’s norms on the second homology of Stallings’ fibrations. It is shown that Thurston’s norm is a matter of pure algebra, if one looks at the Bratteli diagram of an AF C∗-algebra attached to measured geodesic laminations on a compact surface of genus greater or equal to 2. This approach leads to computationa...

The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the matrix norms. In turn this is used to prove that the algebra of left adjointable mappings of a dual operator space X is a von Neumann algebra. If in addition X is...

The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the matrix norms. In turn this is used to prove that the algebra of left adjointable mappings of a dual operator space X is a von Neumann algebra. If in addition X is...

We estimate the norms of many matrix coefficients of irreducible uniformly bounded representations of SL(2, R) as completely bounded multipliers of the Fourier algebra. Our results suggest that the known inequality relating the uniformly bounded norm of a representation and the completely bounded norm of its coefficients may not be optimal.