###### On Quasi-Class A Operators

.E.; Han, Y.M. - Weyl’s theorem for algebraically paranormal operators , Integral Equations Operator Theory, 47 (2003), 307-314. 10. Coburn, L.A. - Weyl’s theorem for nonnormal operators , Michigan Math. J., 13 (1966), 285-288. 11. Conway, John B. - Subnormal Operators. Research Notes in Mathematics, 51, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1981. 12. Cha, H.K. - An extension of Fuglede-Putnam theorem to quasihyponormal operators using a Hilbert-Schmidt operator, Youngnam Math. J., 1 (1994), 73

###### Trace inequalities of Cassels and Grüss type for operators in Hilbert spaces

## Abstract

Some trace inequalities of Cassels type for operators in Hilbert spaces are provided. Applications in connection to Grüss inequality and for convex functions of selfadjoint operators are also given.

###### Reverse Jensen’s type Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

## Abstract

Some reverse Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces are provided. Applications for some convex functions of interest and reverses of Hölder and Schwarz trace inequalities are also given.

###### Controlled G-Frames and Their G-Multipliers in Hilbert spaces

## Abstract

Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are opera- tors that combine (frame-like) analysis, a multiplication with a fixed sequence ( called the symbol) and synthesis. One of the last extensions of frames is weighted and controlled frames that introduced by P.Balazs, J-P. Antoine and A. Grybos to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Also g-frames are the most popular generalization of frames that include almost all of the frame extensions. In this manuscript the concept of the controlled g- frames will be defined and we will show that controlled g-frames are equivalent to g-frames and so the controlled operators C and C' can be used as preconditions in applications. Also the multiplier operator for this family of operators will be introduced and some of its properties will be shown.

###### Vector norm inequalities for power series of operators in Hilbert spaces

References [1] H. Araki and S. Yamagami, An inequality for Hilbert-Schmidt norm, Commun. Math. Phys. 81 (1981), 89-96. [2] R. Bhatia, First and second order perturbation bounds for the operator absolute value, Linear Algebra Appl. 208/209 (1994), 367-376. [3] R. Bhatia, Perturbation bounds for the operator absolute value. Linear Algebra Appl. 226/228 (1995), 639-645. [4] R. Bhatia, D. Singh and K. B. Sinha, Differentiation of operator functions and perturbation bounds. Comm. Math. Phys. 191 (1998), no. 3, 603-611. [5] R. Bhatia, Matrix Analysis, Springer

###### A Review of Feature Selection and Its Methods

. 671-676. 65. Gretton, A., O. Bousquet, A. Smola, B. Schölkopf. Measuring Statistical Dependence with Hilbert-Schmidt Norms. – Springer, 2005, pp. 63-78. 66. Tutkan, M., M. C. Ganiz, S. Akyokuş. Helmholtz Principle Based Supervised and Unsupervised Feature Selection Methods for Text Mining. – Inf. Process. Manag., Vol. 52 , September 2016, No 5, pp. 885-910. 67. Balinsky, A., H. Balinsky, S. Simske. On the Helmholtz Principle for Data Mining. – Hewlett-Packard Dev. Company, LP, 2011. 68. Desolneux, A., L. Moisan, J.-M. Morel. From Gestal

###### Controllability for neutral stochastic functional integrodifferential equations with infinite delay

{array}{} \displaystyle \mathfrak{B} \end{array}$ defined axiomatically (see Section 2 ); F , h : J × B → H $\begin{array}{} \displaystyle F, h : J \times \mathfrak{B} \rightarrow H \end{array}$ are the measurable mappings in H -norm, and G : J × J × B → L Q ( K , H ) ( L Q ( K , H ) $\begin{array}{} \displaystyle G : J \times J \times \mathfrak{B} \rightarrow L_Q(K , H ) (L_Q (K, H) \end{array}$ denotes the space of all Q -Hilbert-Schmidt operators from K into H , which is going to be defined below) is a measurable mapping in L Q ( K , H )-norm. The control function