We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...

We solve two open problems: first we prove a conjecture of Bondal and Van den Bergh, showing that the category $\mathbf{D}^{\mathrm{perf}}(X)$ is strongly generated whenever $X$ quasicompact, separated scheme, admitting cover by affine subsets $\mathrm{Spec}(R_i)$ with each $R_i$ finite global dimension. also that, for noetherian scheme type over an excellent dimension $\le 2$, derived $\mathbf...

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

‎in this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎to this end‎, ‎we aim to replace the field of scalars $ mathbb{r} $ by self-adjoint elements of a commutative $ c^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎first‎, ‎we put forward the concept of operator-valued tensors and extend semi-riemannian...

A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...