In [7, Proposition 1, Remark 1] the authors present two other forms of the Schwarz inequality in semi-inner -module, one for positive linear functional on : (2.5).
In this paper, we simplify one of the required conditions for F (Remark 3.1) and describe a large class of such functions F (Proposition 3.1, Remark 3.2 and Remark 3.3).
In [[11], Proposition 1, Remark 1] the authors present two other forms of the Schwarz inequality in semi-inner A -module X, one for a positive linear functional φ on A : φ ( 〈 x, y 〉 〈 y, x 〉 ) ≤ φ 〈 x, x 〉 r 〈 y, y 〉, (2.3).
C is an arbitrary proposition or factor.
(The presented proof of uniqueness of is somewhat long and involved. Indeed, the referee has remarked that the uniqueness can be obtained directly from [21, Proposition ].) Remark 3.2.
Proposition 3.6 and Remark 3.7 show that increasing the profit rate or decreasing the farming cost (β or p) increases τ * since harvesting (and selling) the more grown organisms results in more profitable.
Remark 8 Using a triangular form of −A (like Jordan's one) (see, e.g., [[4], Proposition 6.14 and Remark 6.26]), it is possible to compute explicitly a constant c s.t.
IfMis non-compact, then we define the weighted counting functionNM, w(T) via the inverse Laplace transform from which one can express the weighted counting function in terms of spectral data associated toM(see Proposition 5.1 and Remark 5.2).
Proposition 1 (See Remark 2.1 in [35]).
end{aligned} By Proposition 2.2(1) and Remark 2.3 we get: Case (i).
Case 1. If, then from (i) of Proposition 2.2 and Remark 2.5, we have (2.29).
