1. CMB Online first
 Moslehian, Mohammad Sal; Zamani, Ali

Characterizations of operator BirkhoffJames orthogonality
In this paper, we obtain some characterizations of the (strong)
BirkhoffJames orthogonality for elements of Hilbert $C^*$modules
and certain elements of $\mathbb{B}(\mathscr{H})$.
Moreover, we obtain a kind of Pythagorean relation for bounded
linear operators.
In addition, for $T\in \mathbb{B}(\mathscr{H})$ we prove that if the
norm attaining
set $\mathbb{M}_T$ is a unit sphere of some finite dimensional
subspace $\mathscr{H}_0$ of $\mathscr{H}$ and $\T\_{{{\mathscr{H}}_0}^\perp}
\lt \T\$, then for every $S\in\mathbb{B}(\mathscr{H})$, $T$ is the strong
BirkhoffJames orthogonal to $S$ if and only if there exists
a unit vector $\xi\in {\mathscr{H}}_0$ such that $\T\\xi =
T\xi$ and $S^*T\xi = 0$.
Finally, we introduce a new type of approximate orthogonality
and investigate this notion in the setting of inner product $C^*$modules.
Keywords:Hilbert $C^*$module, BirkhoffJames orthogonality, strong BirkhoffJames orthogonality, approximate orthogonality Categories:46L05, 46L08, 46B20 

2. CMB 2014 (vol 58 pp. 207)
 Moslehian, Mohammad Sal; Zamani, Ali

Exact and Approximate Operator Parallelism
Extending the notion of parallelism we introduce the concept of
approximate parallelism in normed spaces and then substantially
restrict ourselves to the setting of Hilbert space operators endowed
with the operator norm. We present several characterizations of the
exact and approximate operator parallelism in the algebra
$\mathbb{B}(\mathscr{H})$ of bounded linear operators acting on a
Hilbert space $\mathscr{H}$. Among other things, we investigate the
relationship between approximate parallelism and norm of inner
derivations on $\mathbb{B}(\mathscr{H})$. We also characterize the
parallel elements of a $C^*$algebra by using states. Finally we
utilize the linking algebra to give some equivalence assertions
regarding parallel elements in a Hilbert $C^*$module.
Keywords:$C^*$algebra, approximate parallelism, operator parallelism, Hilbert $C^*$module Categories:47A30, 46L05, 46L08, 47B47, 15A60 
