Paranormal measurable operators affiliated with a semifinite von Neumann algebra. II

Positivity - Let $${{\mathcal {M}}}$$ be a von Neumann algebra of operators on a Hilbert space $${\mathcal {H}}$$ and $$\tau $$ be a faithful normal semifinite trace on $$\mathcal {M}$$ . Let...     

On dualization of a result of Bryce and Cossey theory

Acta Mathematica Hungarica - Let $$\sigma$$ be a partition of the set of all primes $$\mathbb{P}$$ . Let G be a finite group and $$\mathfrak{F}$$ be a Fitting class of finite groups. In the theory...     

Projections of modular forms on Eisenstein series and its application to Siegel’s formula

The Ramanujan Journal - Let $$k \ge 2$$ and N be positive integers and let $$\chi $$ be a Dirichlet character modulo N. Let f(z) be a modular form in $$M_k(\Gamma _0(N),\chi )$$ . Then we have a...     

On the Second Smallest and the Largest Normalized Laplacian Eigenvalues of a Graph

Acta Mathematicae Applicatae Sinica, English Series - Let G be a simple connected graph with order n. Let $$\mathcal{L}(G)$$ and $$\mathcal{Q}(G)$$ be the normalized Laplacian and normalized...     

Numerical semigroups bounded by the translation of a plane monoid

Aequationes mathematicae - Let $$\mathbb {N}$$ be the set of nonnegative integer numbers. A plane monoid is a submonoid of $$(\mathbb {N}^2,+)$$ . Let M be a plane monoid and $$p,q\in \mathbb {N}$$...     

Normal bundles of rational curves in projective space

Mathematische Zeitschrift - Let $$b_{\bullet }$$ be a sequence of integers $$1 < b_1 \le b_2 \le \cdots \le b_{n-1}$$ . Let $${\text {M}}_e(b_{\bullet })$$ be the space parameterizing...     

Asymptotics for the Taylor coefficients of certain infinite products

The Ramanujan Journal - Let $$(m_1,\ldots ,m_J)$$ and $$(r_1,\ldots ,r_J)$$ be two sequences of J positive integers satisfying $$1\le r_j< m_j$$ for all $$j=1,\ldots ,J$$ . Let $$(\delta...     

Schatten class Hankel and $$\overline{\partial }$$ ∂ ¯ -Neumann operators on pseudoconvex domains in $$\mathbb {C}^{n}$$ C n

Monatshefte für Mathematik - Let $$\Omega $$ be a $$C^2$$ -smooth bounded pseudoconvex domain in $$\mathbb {C}^n$$ for $$n\ge 2$$ and let $$\varphi $$ be a holomorphic function on $$\Omega $$...     

On the Root-Class Residuality of Certain Free Products of Groups with Normal Amalgamated Subgroups

Russian Mathematics - Let $${\cal K}$$ be a root class of groups closed under taking quotient groups, G be a free product of groups A and B with amalgamated subgroups H and K. Let also H be normal...     

Certain density theorems applied to the embeddability of iteration semigroups

Aequationes mathematicae - Let A be an additive semigroup of real numbers the additive group generated by which is non-cyclic. Let $$I=(a,b)$$ be an open interval and $$\mathcal {A}=\left\{...     

Representation of zero-sum invariants by sets of zero-sum sequences over a finite abelian group

Periodica Mathematica Hungarica - Let G be an additive finite abelian group. For a sequence T over G and $$g\in G$$ , let $$\mathrm {v}_{g}(T)$$ denote the multiplicity of g in T. Let $$\mathcal...     

Reductions of the strict KP hierarchy

Theoretical and Mathematical Physics - Let $$R$$ be a commutative complex algebra and $$ \partial $$ be a $$ \mathbb{C} $$ -linear derivation of $$R$$ such that all powers of $$ \partial $$ are...     

On Weak Well-posedness of the Nearest Point and Mutually Nearest Point Problems in Banach Spaces

Let G be a nonempty closed subset of a Banach space X. Let B(X) be the family of nonempty bounded closed subsets of X endowed with the Hausdorff distance and ■, where the closure is taken in the metric space(B(X), H). For x ∈ X and F ∈ BG(X), we denote the nearest point problem inf ■ by min(x, G) and the mutually nearest point problem inf■ by min(F, G). In this paper, parallel to well-posedness of the problems min(x, G) and min(F, G) which are defined by De Blasi et al., we further introduce the weak well-posedness of the problems min(x, G) and min(F, G). Under the assumption that the Banach space X has some geometric properties, we prove a series of results on weak well-posedness of min(x, G) and min(F, G). We also give two sufficient conditions such that two classes of subsets of X are almost Chebyshev sets.     

Characterizing linear mappings through zero products or zero Jordan products

Periodica Mathematica Hungarica - Let $${\mathcal {A}}$$ be a $$*$$ -algebra and $${{\mathcal {M}}}$$ be a $$*$$ - $${\mathcal {A}}$$ -bimodule. We study the local properties of $$*$$ -derivations...     

On conditional expectations in $$L^p(\mu ;L^q(\nu ;X))$$ L p ( μ ; L q ( ν ; X ) )

Positivity - Let $$(A,{\mathscr {A}},\mu )$$ and $$(B,{\mathscr {B}},\nu )$$ be probability spaces, let $${\mathscr {F}}$$ be a sub- $$\sigma $$ -algebra of the product $$\sigma $$ -algebra...     

On triviality of the reduced Whitehead group over Henselian fields

Let F be a Henselian field of q-cohomological dimension 3, where q is a prime. Let $$\Gamma _F$$ be the totally ordered Abelian value group of F and let D be a central division algebra over F of index a power of q such that the characteristic of the residue field $$\overline{F}$$ is coprime to q. We show that when $$1\le \dim _{{\mathbb {F}}_q}(\Gamma _F/q\Gamma _F)\le 3$$ , the reduced Whitehead group of D is trivial.     

Multiplier completion of Banach algebras with application to quantum groups

Archiv der Mathematik - Let $${{\mathcal {A}}}$$ be a Banach algebra and let $$\varphi $$ be a non-zero character on $${{\mathcal {A}}}$$ . Suppose that $${{\mathcal {A}}}_M$$ is the closure of the...     

The decomposition of permutation module for infinite Chevalley groups

Let G be a connected reductive group defined over F_q, the finite field with q elements. Let B be a Borel subgroup defined over F_q. In this paper, we completely determine the composition factors of the induced module M(tr) = kG ■tr(where tr is the trivial B-module) for any field k.     

A note on strong skew Jordan product preserving maps on von Neumann algebras

Periodica Mathematica Hungarica - Let $$\mathcal {A}$$ be a von Neumann algebra acting on the complex Hilbert space $$\mathcal {H}$$ and $$\Phi {:}\,\mathcal {A} \longrightarrow \mathcal {A}$$ be a...     

On $$A_1^2$$ A 1 2 restrictions of Weyl arrangements

Journal of Algebraic Combinatorics - Let $$\mathcal {A}$$ be a Weyl arrangement in an $$\ell $$ -dimensional Euclidean space. The freeness of restrictions of $$\mathcal {A}$$ was first settled by a...