相关论文: Birkhoff-James orthogonality in certain tensor pro…
In this article, we discuss the relationship between Birkhoff-James orthogonality of elementary tensors in the space $L^{p}(\mu)\otimes^{\Delta_{p}}X,\; (1\leq p<\infty)$ with the individual elements in their respective spaces, where $X$ is…
We explore Birkhoff-James orthogonality of two elements in a complex Banach space by using the directional approach. Our investigation illustrates the geometric distinctions between a smooth point and a non-smooth point in a complex Banach…
Let $X$ be a complex Banach space and $x,y\in X$. By definition, we say that $x$ is Birkhoff-James orthogonal to $y$ if $ \|x+\lambda y\|_{X} \geq \|x\|_{X}$ for all $\lambda \in \mathbb{C}$. We prove that $x$ is Birkhoff-James orthogonal…
We study Birkhoff-James orthogonality and isosceles orthogonality of bounded linear operators between Hilbert spaces and Banach spaces. We explore Birkhoff-James orthogonality of bounded linear operators in light of a new notion introduced…
This paper deals with study of Birkhoff-James orthogonality of a linear operator to a subspace of operators defined between arbitrary Banach spaces. In case the domain space is reflexive and the subspace is finite dimensional we obtain a…
We study Birkhoff-James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in normed linear spaces and some related geometric ideas, we generalize and…
We study Birkhoff-James orthogonality and its local symmetry in some sequence spaces namely $\ell_p,$ for $1\leq p\leq\infty$, $p\neq2$, $c$, $c_0$ and $c_{00}$. Using the characterization of the local symmetry of Birkhoff-James…
In the last few decades, the concept of Birkhoff-James orthogonality has been used in several applications. In this survey article, the results known on the necessary and sufficient conditions for Birkhoff-James orthogonality in certain…
We use Birkhoff-James' orthogonality in Banach spaces to provide new conditions for the converse of the classical Riesz's representation theorem.
We characterize Birkhoff-James orthogonality of continuous vector-valued functions on a compact topological space. As an application of our investigation, Birkhoff-James orthogonality of real bilinear forms are studied. This allows us to…
In this paper, we obtain some characterizations of the (strong) Birkhoff--James orthogonality for elements of Hilbert $C^*$-modules and certain elements of $\mathbb{B}(\mathscr{H})$. Moreover, we obtain a kind of Pythagorean relation for…
We study the norm derivatives in the context of Birkhoff-James orthogonality in real Banach spaces. As an application of this, we obtain a complete characterization of the left-symmetric points and the right-symmetric points in a real…
We study best approximations in Banach spaces via Birkhoff-James orthogonality of functionals. To exhibit the usefulness of Birkhoff-James orthogonality techniques in the study of best approximation problems, some algorithms and distance…
We study Birkhoff-James orthogonality and its pointwise symmetry in commutative $C^*$ algebras, i.e., the space of all continuous functions defined on a locally compact Hausdorff space that vanish at infinity. We use this characterization…
In this paper we study Birkhoff-James Orthogonality for biadjoints of operators. We partly solve the problem, if an operator is orthogonal to the space of operators valued in a subspace, when the is the norm of biadjoint is attained at a…
In this paper, we extend the investigations regarding Birkhoff-James orthogonality of linear operators to bounded continuous functions on metric spaces. We introduce Birkhoff-James extensions of continuous functions and study them in…
Real smooth three-dimensional or higher Banach spaces are isomorphic with respect to the nonlinear structure of Birkhoff-James orthogonality if and only if they are isometrically isomorphic. Moreover, using smooth Radon planes and…
In this paper we characterize Birkhoff-James orthogonality of linear operators defined on a finite dimensional real Banach space $ \mathbb{X}. $ We also explore the symmetry of Birkhoff-James orthogonality of linear operators defined on $…
The main aim of this paper is to provide characterizations of Birkhoff-James orthogonality (BJ-orthogonality in short) in a number of families of Banach spaces in terms of the elements of significant subsets of the unit ball of their dual…
We study the smoothness and the norm attainment of bounded bilinear operators between Banach spaces, using the concepts of Birkhoff-James orthogonality and semi-inner-products. In the finite-dimensional case, we characterize Birkhoff-James…