Let X and Y be Banach spaces. The main goal of this monograph is to study bounded linear
operators GW X! Y satisfying that for every other bounded linear operator TW X! Y there is a …

The diametral strong diameter 2 property of Banach spaces is the same as the Daugavet
property Page 1 PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 149 …

Lipschitz slices and the Daugavet equation for Lipschitz operators Page 1 PROCEEDINGS
OF THE AMERICAN MATHEMATICAL SOCIETY Volume 143, Number 12, December 2015 …

We introduce a second numerical index for real Banach spaces with non-trivial Lie algebra,
as the best constant of equivalence between the numerical radius and the quotient of the …

We show that for spaces with 1–unconditional bases lushness, the alternative Daugavet
property and numerical index 1 are equivalent. In the class of rearrangement invariant (ri) …

We prove that every JB⁎-triple E (in particular, every C⁎-algebra) satisfying the Daugavet
property also satisfies the stronger polynomial Daugavet property, that is, every weakly …

We construct an example of a Banach space which is not lush, but whose dual space is lush.
This example shows that lushness is not equivalent to numerical index one. A …

We show that the numerical index of any operator ideal is less than or equal to the minimum
of the numerical indices of the domain space and the range space. Further, we show that the …

We introduce slicely countably determined points (SCD points) of a bounded and convex
subset of a Banach space which extends the notions of denting points, strongly regular …

We study the presence of L-orthogonal elements in connection with Daugavet centers and
narrow operators. We prove that if dens (Y)⩽ ω 1 and G: X⟶ Y is a Daugavet center with …