P-Norm B-Tensors and p-Norm $$B_0$$-Tensors

Abstract

We propose two new classes of tensors: p-norm B-tensors and p-norm $$B_0$$ -tensors, and discuss their relationships with P( $$P_0$$ )-tensors and MB ( $$MB_0$$ )-tensors. We prove that a real symmetric p-norm B( $$B_0$$ )-tensor can always be decomposed into the sum of a p-norm strictly diagonally dominant (p-norm diagonally dominant) Z-tensor and several positive multiples of partially all one tensors. Specially, when the order of the tensor is even, we obtain that the corresponding real symmetric p-norm B( $$B_0$$ )-tensor is positive (semi-)definite. This gives a checkable sufficient condition for the positive (semi-)definite tensors.