Inequalities for unitarily invariant norms
نویسندگان
چکیده
This paper aims to discuss some inequalities for unitarily invariant norms. We obtain several inequalities for unitarily invariant norms.
منابع مشابه
Cauchy-schwarz Inequalities Associated with Positive Semideenite Matrices
Using a quasilinear representation for unitarily invariant norms, we prove a basic inequality: Let A = L X X M be positive semideenite, where X 2 M m;n. Then k jX j p k 2 kL p k kM p k for all p > 0 and all unitarily invariant norms k k. We show how several inequalities of Cauchy-Schwarz type follow from this bound and obtain a partial analog of our results for l p norms.
متن کاملSubmultiplicativity Vs Subadditivity for Unitarily Invariant Norms
Let A,B be nonzero positive semidefinite matrices. We prove that ‖AB‖ ‖A‖ ‖B‖ ≤ ‖A + B‖ ‖A‖+ ‖B‖ , ‖A ◦B‖ ‖A‖ ‖B‖ ≤ ‖A + B‖ ‖A‖+ ‖B‖ for any unitarily invariant norm with ‖diag(1, 0, . . . , 0)‖ ≥ 1. Some related inequalities are derived. AMS classification: 15A60, 15A45
متن کاملA Structure Theorem for the Polars of Unitarily Invariant Norms
The unitarily invariant norms of matrices, or operators, are essentially the symmetric norms of their singular values. A subclass of these norms depending upon only a few largest of the singular values is considered, and the polars of these norms are characterized. The result is then used to obtain generalizations of some well-known inequalities. The implications for operators on infinite-dimen...
متن کاملSome Inequalities for Unitarily Invariant Norms
This paper aims to present some inequalities for unitarily invariant norms. In section 2, we give a refinement of the Cauchy-Schwarz inequality for matrices. In section 3, we obtain an improvement for the result of Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203-211]. In section 4, we establish an improved Heinz inequality for the Hilbert-Schmidt norm. Finally, we present an inequality...
متن کاملOn Some New Fractional Type Heinz Inequalities
The authors shall discuss Heinz inequalities involving Riemann-Liouville fractional integrals for certain unitarily invariant norms. By using the convexity of function and fractional Hermit-Hadamard integral inequality, some refinements of Heinz inequalities are derived.
متن کامل