This monograph is devoted to the study of spear operators that is bounded linear operators G
between Banach spaces X and Y satisfying that for every other bounded linear operator T:X Y
there exists a modulus-one scalar such that G+ T = 1 + T .This concept extends the properties
of the identity operator in those Banach spaces having numerical index one. Many examples among
classical spaces are provided being one of them the Fourier transform on L . The relationships
with the Radon-Nikodým property with Asplund spaces and with the duality and some isometric
and isomorphic consequences are provided. Finally Lipschitz operators satisfying the Lipschitz
version of the equation above are studied. The book could be of interest to young researchers
and specialists in functional analysis in particular to those interested in Banach spaces and
their geometry. It is essentially self-contained and only basic knowledge of functional
analysis is needed.
