Multipliers of weighted spaces
Multipliers on Banach algebras
Multipliers on complex Banach spaces
Multipliers on Schwartz spaces of some Lie groups
Multipliers on some Lorentz spaces.
Multipliers, self-induced and dual Banach algebras [Book]
Multipliers with closed range on commutative semisimple Banach algebras
Let A be a commutative semisimple Banach algebra, Δ(A) its Gelfand spectrum, T a multiplier on A and T̂ its Gelfand transform. We study the following problems. (a) When is δ(T) = inf{|T̂(f)|: f ∈ Δ(A), T̂(f) ≠ 0} > 0? (b) When is the range T(A) of T closed in A and does it have a bounded approximate identity? (c) How to characterize the idempotent multipliers in terms of subsets of Δ(A)?
Multiplying balls in the space of continuous functions on [0,1]
Let C denote the Banach space of real-valued continuous functions on [0,1]. Let Φ: C × C → C. If Φ ∈ +, min, max then Φ is an open mapping but the multiplication Φ = · is not open. For an open ball B(f,r) in C let B²(f,r) = B(f,r)·B(f,r). Then f² ∈ Int B²(f,r) for all r > 0 if and only if either f ≥ 0 on [0,1] or f ≤ 0 on [0,1]. Another result states that Int(B₁·B₂) ≠ ∅ for any two balls B₁ and B₂ in C. We also prove that if Φ ∈ +,·,min,max, then the set is residual whenever E is residual in...
Multismoothness in Banach spaces.
Multivalued superposition operators
Multi-valued superpositions [Book]
Multivariate Interpolation and the Radon Transform.
Murphy's "Positive definite kernels and Hilbert C*-modules" reorganized
The paper the title refers to is that in Proceedings of the Edinburgh Mathematical Society, 40 (1997), 367-374. Taking it as an excuse we intend to realize a twofold purpose: 1° to atomize that important result showing by the way connections which are out of favour, 2° to rectify a tiny piece of history. The objective 1° is going to be achieved by adopting means adequate to goals; it is of great gravity and this is just Mathematics. The other, 2°, comes...
Musielak-Orlicz algebras
Musielak-Orlicz spaces and prediction problems
By a harmonizable sequence of random variables we mean the sequence of Fourier coefficients of a random measure M: (n = 0,±1,...) The paper deals with prediction problems for sequences Xₙ(M) for isotropic and atomless random measures M. The crucial result asserts that the space of all complex-valued M-integrable functions on the unit interval is a Musielak-Orlicz space. Hence it follows that the problem for Xₙ(M) (n = 0,±1,...) to be deterministic is in fact an extremal problem of Szegö’s type...
Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates
Let X be a metric space with doubling measure and L a one-to-one operator of type ω having a bounded H∞ -functional calculus in L2(X) satisfying the reinforced (pL; qL) off-diagonal estimates on balls, where pL ∊ [1; 2) and qL ∊ (2;∞]. Let φ : X × [0;∞) → [0;∞) be a function such that φ (x;·) is an Orlicz function, φ(·;t) ∊ A∞(X) (the class of uniformly Muckenhoupt weights), its uniformly critical upper type index l(φ) ∊ (0;1] and φ(·; t) satisfies the uniformly reverse Hölder inequality of order...
Musielak-Orlicz-Sobolev spaces on metric measure spaces
Our aim in this paper is to study Musielak-Orlicz-Sobolev spaces on metric measure spaces. We consider a Hajłasz-type condition and a Newtonian condition. We prove that Lipschitz continuous functions are dense, as well as other basic properties. We study the relationship between these spaces, and discuss the Lebesgue point theorem in these spaces. We also deal with the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz spaces. As an application of the boundedness of the Hardy-Littlewood...
Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces
We define and study Musielak-Orlicz-Sobolev spaces with zero boundary values on any metric space endowed with a Borel regular measure. We extend many classical results, including completeness, lattice properties and removable sets, to Musielak-Orlicz-Sobolev spaces on metric measure spaces. We give sufficient conditions which guarantee that a Sobolev function can be approximated by Lipschitz continuous functions vanishing outside an open set. These conditions are based on Hardy type inequalities....
Mutations of C*-algebras and quasiassociative JB*-algebras
M-weak and L-weak compactness of b-weakly compact operators
We characterize Banach lattices under which each b-weakly compact (resp. b-AM-compact, strong type (B)) operator is L-weakly compact (resp. M-weakly compact).