Norm inequalities involving accretive-dissipative 2 × 2 block matrices

Norm inequalities for submultiplicative functions involving contraction sector $2 \times 2$ block matrices

“…Note that if A is accretive-dissipative, then W (e -iπ 4 A) ⊆ S π 4 . Recently this class of matrices has been studied by researchers partly due to the fact that it contains the class of positive semidefinite matrices (see, e.g., [1,[11][12][13][14][15][16][17]).…”

“…There are many other properties on this class of functions; see [12,18]. A nonnegative function f ∈ C on the interval [0, ∞) is said to be submultiplicative if f (ab) ≤ f (a)f (b) whenever a, b ∈ [0, ∞).…”

“…A nonnegative function f ∈ C on the interval [0, ∞) is said to be submultiplicative if f (ab) ≤ f (a)f (b) whenever a, b ∈ [0, ∞). Recently, some unitarily invariant norm inequalities for submultiplicative functions of accretive-dissipative matrices have been shown in [12] and [13].…”

“…In [12] and [13], some unitarily invariant norms for accretive-dissipative matrices involving a special class of functions have been shown. In this section, we present inequalities for sector block matrices involving the class of function.…”

On the logarithmic mean of accretive matrices

“…If A is positive definite, then we say A is accretive. This class of matrices and its subclass, viz, accretive-dissipative matrices, are receiving much attention over the past few years; see [4,[11][12][13][14][15][16]19].…”