On some equivalent metrics for bounded operators on Hilbert space

Author:
Fuad Kittaneh

Journal:
Proc. Amer. Math. Soc. **110** (1990), 789-798

MSC:
Primary 47A30; Secondary 47B10, 47B15

DOI:
https://doi.org/10.1090/S0002-9939-1990-1027097-6

MathSciNet review:
1027097

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Several operator norm inequalities concerning the equivalence of some metrics for bounded linear operators on Hilbert space are given. In addition, some related inequalities for the Hilbert-Schmidt norm are presented.

**[1]**T. Ando,*Topics on operator inequalities*, preprint, Research Institute of Applied Electricity, Hokkaido, Sapporo, Japan. MR**0482378 (58:2451)****[2]**-,*Comparison of norms**and*, Math. Z.**197**(1988), 403-409. MR**926848 (90a:47021)****[3]**J. Arazy,*More on convergence in unitary matrix spaces*, Proc. Amer. Math. Soc.**83**(1981), 44-48. MR**619978 (82f:46009)****[4]**R. Bhatia,*Perturbation inequalities for the absolute value map in norm ideals of operators*, J. Operator Theory**19**(1988), 129-136. MR**950829 (89g:47010)****[5]**R. Bhatia and F. Kittaneh,*On some perturbation inequalities for operators*, Linear Algebra Appl.**106**(1988), 271-279. MR**951838 (90f:47007)****[6]**-,*Norm inequalities for partitioned operators and an application*, preprint.**[7]**E. B. Davies,*Lipschitz continuity of functions of operators in the Schatten classes*, J. London Math. Soc.**37**(1988), 148-157. MR**921753 (89c:47009)****[8]**T. Kato,*Perturbation theory for linear operators*, 2nd ed., Springer-Verlag, New York, 1976. MR**0407617 (53:11389)****[9]**W. E. Kaufman,*Representing a closed operator as a quotient of continuous operators*, Proc. Amer. Math. Soc.**72**(1978), 531-534. MR**509249 (80a:47027)****[10]**-,*Closed operator and pure contractions in Hilbert space*, Proc. Amer. Math. Soc.**87**(1983), 83-87. MR**677237 (84c:47019)****[11]**-,*A stronger metric for closed operators in Hilbert space*, Proc. Amer. Math. Soc.**90**(1984), 83-87. MR**722420 (85a:47010)****[12]**F. Kittaneh,*On Lipschitz functions of normal operators*, Proc. Amer. Math. Soc.**94**(1985), 416-418. MR**787884 (87b:47021)****[13]**-,*Inequalities for the Schatten*. II, Glasgow Math. J.**29**(1987), 99-104. MR**876154 (88d:47027)****[14]**-,*Inequalities for the Schatten**-norm*. IV, Commun. Math. Phys.**106**(1986), 581-585. MR**860311 (88j:47010)****[15]**-,*On the continuity of the absolute value map in the Schatten classes*, Linear Algebra Appl.**118**(1989), 61-68. MR**995365 (91d:47007)****[16]**F. Kittaneh and H. Kosaki,*Inequalities for the Schatten**-norm*. V, Publ. Res. Inst. Math. Sci. Kyoto Univ.**23**(1987), 433-443. MR**890926 (88h:47011)****[17]**R. Schatten,*Norm ideals of completely continuous operators*, Springer-Verlag, Berlin, 1960. MR**0119112 (22:9878)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
47A30,
47B10,
47B15

Retrieve articles in all journals with MSC: 47A30, 47B10, 47B15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1027097-6

Keywords:
Equivalent metrics,
positive operator,
operator monotone function,
operator norm,
Hilbert-Schmidt norm

Article copyright:
© Copyright 1990
American Mathematical Society