Sentence examples for operators class from inspiring English sources

This result was extended to p-quasihyponormal operators, class A operators, ∗-class A operators, log-hyponormal operators and class A ( s, t ) operators ( ( | T ∗ | t | T | 2 s | T ∗ | t ) t s + t ≥ | T ∗ | 2 t, s, t > 0 ) in [20 23], respectively.

Furuta et al. [1] introduced a very interesting class of bounded linear Hilbert space operators: class defined by | T 2 | ≥ | T | 2, which is called the absolute value of T, and they showed that the class A is a subclass of paranormal operators.

Recently Jeon and Kim [3] have considered the following new class of operators: we say that an operator T ∈ B ( H ) belongs to the ∗-class A if | T 2 | ≥ | T ∗ | 2. For brevity, we shall denote the classes of hyponormal operators, paranormal operators, ∗-paranormal operators, class A operators, and ∗-class A operators by ℋ, PN, P N ∗, A and A ∗ respectively.

In order to discuss the relations between paranormal and -hyponormal and log-hyponormal operators, Furuta et al. [13] introduced a very interesting class of bounded linear Hilbert space operators: class A defined by, where which is called the absolute value of and they showed that class A is a subclass of paranormal and contains -hyponormal and log-hyponormal operators.

This operation is supported by the GIST index operator class for cube values and therefore avoids linear scans of all USRCAT moments.

Recently, Han and Na introduced a new operator class which contains the classes of paranormal operators and quasi-class A operators [4].

Obviously, the nonexpansive mapping class is a proper subclass of the strict pseudo-contraction class and the Lipschitzian operator class is a proper subclass of the boundedly Lipschitzian operator class, respectively.

An operator T ∈ B ( H ) is said to be paranormal if T x 2 ≤ T 2 x x for all x ∈ H. Recently, we introduced a new operator class which is a common generalization of paranormal operators and quasi-class A operators [4].

The game brings a new Operator class system to ensure each player has something to do, and should offer 20 classes to make sure each game is a bit different.

Recently Duggal et al. [5] introduced ∗-class A operators (i.e., | T 2 | − | T ∗ | 2 ≥ 0 ) and ∗-paranormal operators (i.e., ∥ T ∗ x ∥ 2 ≤ ∥ T 2 x ∥ ∥ x ∥ for all x ∈ H ); and they proved that a ∗-class A operator is a generalization of hyponormal operator and ∗-class A operators form a subclass of the class of ∗-paranormal operators.

Our operator classes are intrinsically related to the ultradistributional framework so that the bounds on the derivatives of the symbols are controlled by Gevrey type weight sequences.