SOME PROPERTIES OF THE SPHERICAL m-ISOMETRIES

作者：Hedayatian Karim^*; Mohammadi-Moghaddam Amir

来源：Journal of Operator Theory, 2018, 79(1): 55-77.

DOI：10.7900/jot.2016oct31.2149

• m-Isometry
• power regularity
• spherical m-isometry
• d-tuple

A commuting d-tuple T = (T-1 , . . . , T-d) is called a spherical m-isometry if Sigma(m)(j=0)(-1)(j)((m)(j))Q(T)(j)(I)= 0, where Q(T)(A) = Sigma T-d(i=1)i* AT(i) for every bounded linear operator A on a Hilbert space H. Under some assumptions we prove that every power of T is a spherical m-isometry. Also, we study the products of spherical m-isometries when they remain spherical n-isometrics, for a suitable n. Besides, we prove that the spherical m-isometries are power regular and for every proper spherical m-isometry there are linearly independent operators A(0) , . . . , A(m-1) such that Q(T)(n)(I) = Sigma(m-1)(i=0)A(i)n(i) for every n >= 0.

• 出版日期2018