Essentially Invertible Measurable Operators Affiliated to a Semifinite von Neumann Algebra and Commutators

Siberian Mathematical Journal - Suppose that a von Neumann operator algebra  $ {\mathcal{M}} $ acts on a Hilbert space  $ {\mathcal{H}} $ and $ \tau $...     

A Semilattice of Degrees of Computable Metrics

Siberian Mathematical Journal - Under study is the ordering $ {\mathcal{CM}}_{c}({\mathbf{X}}) $ of $ c $ -degrees of computable metrics on a Polish space  $ {\mathbf{X}} $ with...     

The Furstenberg Boundary of Groupoids

Siberian Mathematical Journal - Let $ {\mathcal{G}} $ be a locally compact groupoid. We show that there is a one-to-one correspondence between $ {\mathcal{G}} $ -spaces and the groupoid...     

The Root-Class Residuality of the Fundamental Groups of Certain Graphs of Groups with Central Edge Subgroups

Siberian Mathematical Journal - Consider a class  $ {\mathcal{C}} $ of groups which contains at least one nontrivial group and is closed under subgroups, extensions, and...     

On Nonconstant Pre-Lie Bimodules over $ M_{2}(F) $

Siberian Mathematical Journal - We describe the unital finite-dimensional simple nonconstant bimodules  $ {\mathcal{W}} $ over the matrix algebra  $ M_{2}(F) $ over...     

Formulas for Calculating the $ 3j $ -Symbols of the Representations of the Lie Algebra $ {\mathfrak{gl}}_{3} $ for the Gelfand–Tsetlin Bases

Siberian Mathematical Journal - We give a simple explicit formula for an arbitrary $ 3j $ -symbol for the Lie algebra  $ {\mathfrak{gl}}_{3} $ . The symbol is...     

Locally Finite Groups with Prescribed Structure of Finite Subgroups

Siberian Mathematical Journal - Let  $ {\mathfrak{M}} $ be a set of finite groups. Given a group  $ G $ , denote the set of all subgroups of  $ G $...     

关于${\cal I}$-覆盖映射与1-${\cal I}$-覆盖映射

In this paper,we introduce the concepts of I-covering mappings and 1-I-covering mappings,discuss the difference between sequence-covering and I-covering mappings by some examples.With those concepts,we get some interesting properties of I-covering(1-I-covering)mappings and some characterizations of I-covering(1-I-covering)and compact mapping images of metric spaces.     

Schur–Weyl Theory for C*‐algebras

To each irreducible infinite dimensional representation $(\pi ,\mathcal {H})$ of a C*‐algebra $\mathcal {A}$, we associate a collection of irreducible norm‐continuous unitary representations $\pi _{\lambda }^\mathcal {A}$ of its unitary group ${\rm U}(\mathcal {A})$, whose equivalence classes are parameterized by highest weights in the same way as the irreducible bounded unitary representations of the group ${\rm U}_\infty (\mathcal {H}) = {\rm U}(\mathcal {H}) \cap (\mathbf {1} + K(\mathcal {H}))$ are. These are precisely the representations arising in the decomposition of the tensor products $\mathcal {H}^{\otimes n} \otimes (\mathcal {H}^*)^{\otimes m}$ under ${\rm U}(\mathcal {A})$. We show that these representations can be realized by sections of holomorphic line bundles over homogeneous Kähler manifolds on which ${\rm U}(\mathcal {A})$ acts transitively and that the corresponding norm‐closed momentum sets $I_{\pi _\lambda ^\mathcal {A}}^{\bf n} \subseteq {\mathfrak u}(\mathcal {A})^{\prime }$ distinguish inequivalent representations of this type.     

Finite Groups with Subnormal Residuals of Sylow Normalizers

Siberian Mathematical Journal - Considering a nonempty formation $ {\mathfrak{X}} $ of nilpotent groups, we prove that a group $ G $ is an extension of a nilpotent group by an $...     

Accelerated dynamical approaches for finding the unique positive solution of K S $\mathcal {K}\mathcal {S}$ -tensor equations

Numerical Algorithms - A new class of tensors called $\mathcal {K}\mathcal {S}$ -tensors, which is a subset of non-singular $\mathcal {P}$ -tensors and generalization of ${\mathscr{H}}^{+}$...     

Littlewood-Paley Formulas and Carleson Measures for Weighted Fock Spaces Induced by A ∞ $A_{\infty }$ -Type Weights

Potential Analysis - We obtain Littlewood-Paley formulas for Fock spaces ${\mathcal {F}}_{\beta ,\omega }^{q}$ induced by weights $\omega \in {A}_{\infty }^{restricted} = \cup _{1 \le p <...     

On Unconditional and Absolute Convergence of the Haar Series in the Metric of $ L^{p}[0,1] $ with $ 0

Grigoryan  M. G. 《Siberian Mathematical Journal》2021,62(4):607-615

投影的约化极小模和空间的夹角

Let M and N be nonzero subspaces of a Hilbert space H, and PM and PN denote the orthogonal projections on M and N, respectively. In this note, an exact representation of the angle and the minimum gap of M and N is obtained. In addition, we study relations between the angle, the minimum gap of two subspaces M and N, and the reduced minimum modulus of （I - PN）PM,     

Bochner-Kodaira Techniques on K¨ahler Finsler Manifolds

A horizontal Hodge Laplacian operator $\square_{\mathcal {H}}$ is defined for Hermitian holomorphic vector bundles over PTM on K¨ahler Finsler manifold, and the expression of $\square_{\mathcal {H}}$ is obtained explicitly in terms of horizontal covariant derivatives of the Chern-Finsler connection. The vanishing theorem is obtained by using the $\partial_{\mathcal {H}}\ov{\partial}_{\mathcal {H}}$-method on K¨ahler Finsler manifolds.     

On the Right (Left) Invertible Completions for Operator Matrices

Let ${\mathcal {H}_{1}}Let H₁{\mathcal {H}_{1}} and H₂{\mathcal {H}_{2}} be separable Hilbert spaces, and let A ? B(H₁), B ? B(H₂){A \in \mathcal {B}(\mathcal {H}_{1}),\, B \in \mathcal {B}(\mathcal {H}_{2})} and C ? B(H₂, H₁){C \in \mathcal {B}(\mathcal {H}_{2},\, \mathcal {H}_{1})} be given operators. A necessary and sufficient condition is given for ${\left(\begin{smallmatrix}A &\enspace C\\ X &\enspace B \end{smallmatrix}\right)}${\left(\begin{smallmatrix}A &\enspace C\\ X &\enspace B \end{smallmatrix}\right)} to be a right (left) invertible operator for some X ? B(H₁, H₂){X \in \mathcal {B}(\mathcal {H}_{1},\, \mathcal {H}_{2})}. Furthermore, some related results are obtained.     

Point value characterizations and related results in the full Colombeau algebras \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${{\mathcal {G}}^e(\Omega )}$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${{\mathcal {G}}^d(\Omega )}$\end{document}

We present a point value characterization for elements of the elementary full Colombeau algebra ${\mathcal {G}}^e(\Omega )$ and the diffeomorphism invariant full Colombeau algebra $\mathcal {G}^d(\Omega )$. Moreover, several results from the special algebra ${\mathcal {G}}^s(\Omega )$ about generalized numbers and invertibility are extended to the elementary full algebra.     

Approximate Representation of Bergman Submodules

In the present paper, the author shows that if a homogeneous submodule M of the Bergman module L_a~2(B_d) satisfies P_M-sum from i to ( M_(zi)P_MM*_(zi))≤c/(N + 1)P_M for some number c 0, then there is a sequence {f_j } of multipliers and a positive number c such that c'P_M ≤sum from j to ( M_(fj)M*_(fj))≤ P_M, i.e., M is approximately representable. The author also proves that approximately representable homogeneous submodules are p-essentially normal for p d.     

Right Alternative Unital Bimodules over the Matrix Algebras of Order $ \geq 3 $

Siberian Mathematical Journal - We address the unital right alternative bimodules over the matrix algebras  $ {\mathrm{M}}_{n}(\Phi) $ of order $ n\geq 3 $ , prove that each of these...     

Existence, automatic continuity and invariant submodules of generalized derivations on modules

Let ${\mathcal{A}}$ be a ${\mathbb{C}}$ -algebra, δ be a derivation on ${\mathcal{A}}$ and ${\mathcal{M}}$ be a left ${\mathcal{A}}$ -module. A linear map ${\tau : \mathcal{M} \rightarrow \mathcal{M}}$ is called a generalized derivation relative to δ if ${\tau(am)=a\tau(m)+\delta(a)m\,(a \in \mathcal{A}, m \in \mathcal{M})}$ . In this article first we study the existence of generalized derivations. In particular we show that free modules and projective modules always have nontrivial generalized derivations relative to nonzero derivations of ${\mathcal{A}}$ . Then we investigate the invariance of prime submodules under generalized derivations. Specifically we show that every minimal prime submodule of ${\mathcal{M}}$ is invariant under every generalized derivation. Moreover we obtain analogs of Posner’s theorem for generalized derivations. In the case that ${\mathcal{A}}$ is a Banach algebra and ${\mathcal{M}}$ is a Banach left ${\mathcal{A}}$ -module, we study the existence of continuous generalized derivations and automatic continuity of generalized derivations.