Complex symmetric partial isometries

An operator T \in B(\h) is complex symmetric if there exists a conjugate-linear, isometric involution C:\h\to\h so that $T = CT^*C$. We provide a concrete description of all complex symmetric partial isometries. In particular, we prove that any partial isometry on a Hilbert space of dimension $\leq 4$ is complex symmetric.Comment: 9 page

C∗C^*-algebras generated by truncated Toeplitz operators

We obtain an analogue of Coburn's description of the Toeplitz algebra in the setting of truncated Toeplitz operators. As a byproduct, we provide several examples of complex symmetric operators which are not unitarily equivalent to truncated Toeplitz operators having continuous symbols.Comment: 12 page

Spatial isomorphisms of algebras of truncated Toeplitz operators

We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maximal algebras of truncated Toeplitz operators.Comment: 24 page

Common Cyclic Vectors for Normal Operators

If μis a finite compactly supported measure on C, then the set Sμ of multiplication operators Mᵩ : L2 (μ) --\u3e L2 (μ), Mᵩ f = ᵩ f, where ᵩ ϵ L ∞ (μ) is injective on a set of full μ measure, is the complete set of cyclic multiplication operators on L2 (μ) In this paper, we explore the question as to whether or not Sμ has a common cyclic vecto

Reflexivity properties of T ⊕ 0

AbstractA construction is given of a reflexive operator T acting on a separable Hilbert space H with the property that the direct sum T ⊕ 0 fails to be reflexive. This construction is then used to provide solutions to several other problems which have been studied concerning the direct-sum splitting of operator algebras, Scott Brown's technique, the theory of bitriangular operators, and parareflexivity

Common Cyclic Vectors for Unitary Operators

In this paper, we determine whether or not certain natural classes of unitary multiplication operators on L2(dƟ) have common cyclic vectors. For some classes which have common cyclic vectors, we obtain a classification of these vectors

Effect of cardiometabolic risk factors on hypertension management: a cross-sectional study among 28 physician practices in the United States

<p>Abstract</p> <p>Objective</p> <p>This cross-sectional study sought to determine the prevalence of cardiometabolic risk factor clusters (CMRFCs) and their effect on BP control among hypertensive patients from 28 US physician practices.</p> <p>Methods</p> <p>Each participating practice identified a random sample of 150-300 adults aged ≥ 18 years diagnosed with hypertension. The primary outcome variable was BP control (BP < 140/90 mmHg for non-diabetic and <130/80 mmHg for diabetic patients). CMRFCs included hypertension in addition to obesity, dyslipidemia, and diabetes.</p> <p>Results</p> <p>Overall, 6,527 hypertensive patients were identified for study inclusion. More than half (54.3%) were female, and mean age was 64.7 years. Almost half (48.7%) were obese (BMI ≥ 30 kg/m²). About 1 in every 4 patients (25.3%) had diabetes, and 60.7% had dyslipidemia. Mean blood pressure was 132.5/77.9 mmHg, and 55.0% of all patients had controlled BP; 62.4% of non-diabetic patients, and 33.3% of diabetic hypertensive patients, had BP controlled to recommended levels. Most (81.7%) hypertensive patients had ≥ 1 cardiometabolic risk factor, and 12.2% had all 3 risk factors. As compared to hypertensive patients without additional risk factors, adjusted odds ratios for BP control were significantly lower for all combinations of CMRFCs (ORs 0.15-0.83, all p < 0.04), with the exception of patients who had only dyslipidemia in addition to hypertension (OR = 1.09, p = NS). Prescriber adherence to recommended hypertension treatment guidelines for patients with diabetes, heart failure, or prior myocardial infarction was high. Although patients with risk factors were prescribed more antihypertensive medications than those without, hypertensive patients with all 3 risk factors were prescribed a mean of 2.4 antihypertensive medications compared to 1.7 for those with no risk factors; odds of BP control in these patients, however, was 0.23 [95% CI 0.19-0.29] that of patients with no other CMRFCs.</p> <p>Conclusions</p> <p>Across 28 US practices, only 18% of hypertensive patients did not have any additional cardiometabolic risk factors. The high prevalence of CMRFCs presents a challenge to effective hypertension management.</p

Extensions of operators

We introduce the concept of the extension spectrum of a Hilbert space operator. This is a natural subset of the spectrum which plays an essential role in dealing with certain extension properties of operators. We prove that it has spectral-like properties and satisfies a holomorphic version of the Spectral Mapping Theorem. We establish structural theorems for algebraic extensions of triangular operators which use the extension spectrum in a natural way. The extension spectrum has some properties in common with the Kato spectrum, and in the final section we show how they are different and we examine their inclusion relationships

Truncated Toeplitz Operators on Finite Dimensional Spaces

In this paper, we study the matrix representations of compressions of Toeplitz operators to the finite dimensional model spaces H2ƟBH2, where B is a finite Blaschke product. In particular, we determine necessary and sufficient conditions - in terms of the matrix representation - of when a linear transformation on H2ƟBH2 is the compression of a Toeplitz operator. This result complements a related result of Sarason [6]