On the spectrum of a nonlinear operator associated with calculation of the norm of a linear vector-functional - Burenkov, Victor Ivanovich; Tararykova, Tamara Vasil’evna (Eurasian Mathematical Journal, 2014)
An explicit formula is presented for the norm if \( 1 ≤ p ≤ ∞ \) and for the quasi-norm if \( 0 < p < 1 \) of a linear vector-functional \( L : H → \ell_p \) on a Hilbert space \( H \) and the set of all extremal elements is described. All eigenvalues and eigenvectors of a nonlinear homogeneous operator entering the corresponding Euler’s equation, are written out explicitly.