diff --git a/Project.toml b/Project.toml
index 79dc748..c3c6ffd 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "InfiniteArrays"
 uuid = "4858937d-0d70-526a-a4dd-2d5cb5dd786c"
-version = "0.15.10"
+version = "0.15.11"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
@@ -33,7 +33,7 @@ BlockBandedMatrices = "0.13"
 DSP = "0.7, 0.8"
 FillArrays = "1.0"
 Infinities = "0.1.1"
-LazyArrays = "2.2.3"
+LazyArrays = "2.9.3"
 LinearAlgebra = "1.6"
 SparseArrays = "1.0"
 Statistics = "1.0"
diff --git a/ext/InfiniteArraysBandedMatricesExt.jl b/ext/InfiniteArraysBandedMatricesExt.jl
index bc008a0..9c67792 100644
--- a/ext/InfiniteArraysBandedMatricesExt.jl
+++ b/ext/InfiniteArraysBandedMatricesExt.jl
@@ -3,10 +3,10 @@ using InfiniteArrays, BandedMatrices, LinearAlgebra
 using InfiniteArrays.LazyArrays, InfiniteArrays.ArrayLayouts, InfiniteArrays.FillArrays
 
 import Base: BroadcastStyle, size, getindex, similar, copy, *, +, -, /, \, materialize!, copyto!, OneTo
-import Base.Broadcast: Broadcasted
+import Base.Broadcast: Broadcasted, result_style
 import InfiniteArrays: InfIndexRanges, Infinity, PosInfinity, OneToInf, InfAxes, AbstractInfUnitRange, InfRanges, InfBaseToeplitzLayouts, ConstRowMatrix, PertConstRowMatrix, SymTriPertToeplitz, TriPertToeplitz, ConstRows, PertConstRows, PertTridiagonalToeplitzLayout
 import ArrayLayouts: sub_materialize, MemoryLayout, sublayout, mulreduce, triangularlayout, MatLdivVec, subdiagonaldata, diagonaldata, supdiagonaldata, OnesLayout, _copy_oftype
-import LazyArrays: applybroadcaststyle, applylayout, islazy, islazy_layout, simplifiable, AbstractLazyLayout, PaddedColumns, LazyArrayStyle, ApplyLayout, AbstractLazyBandedLayout, ApplyBandedLayout, BroadcastBandedLayout
+import LazyArrays: applybroadcaststyle, applylayout, islazy, islazy_layout, simplifiable, AbstractLazyLayout, PaddedColumns, LazyArrayStyle, ApplyLayout, AbstractLazyBandedLayout, ApplyBandedLayout, BroadcastBandedLayout, CachedArrayStyle, AbstractLazyArrayStyle
 import BandedMatrices: _BandedMatrix, AbstractBandedMatrix, banded_similar, BandedMatrix, bandedcolumns, BandedColumns, bandeddata, _default_banded_broadcast
 import FillArrays: AbstractFillMatrix, AbstractFill, getindex_value
 
@@ -26,9 +26,11 @@ InfBandCartesianIndices(b::Band) = InfBandCartesianIndices(b.i)
 size(::InfBandCartesianIndices) = (∞,)
 getindex(B::InfBandCartesianIndices, k::Int) = B.b ≥ 0 ? CartesianIndex(k, k+B.b) : CartesianIndex(k-B.b, k)
 
+
 Base.checkindex(::Type{Bool}, ::NTuple{2,OneToInf{Int}}, ::InfBandCartesianIndices) = true
 BandedMatrices.band_to_indices(_, ::NTuple{2,OneToInf{Int}}, b) = (InfBandCartesianIndices(b),)
-BroadcastStyle(::Type{<:SubArray{<:Any,1,<:Any,Tuple{InfBandCartesianIndices}}}) = LazyArrayStyle{1}()
+_lower_style_dim(::Sty) where {Sty} = Sty(Val(1))
+BroadcastStyle(::Type{<:SubArray{<:Any,1,P,Tuple{InfBandCartesianIndices}}}) where {P} = _lower_style_dim(result_style(LazyArrayStyle{1}(), BroadcastStyle(P)))
 
 _inf_banded_sub_materialize(_, V) = V
 function _inf_banded_sub_materialize(::BandedColumns, V)
@@ -296,6 +298,7 @@ for Typ in (:ConstRows, :PertConstRows)
     @eval begin
         sublayout(::$Typ, ::Type{<:Tuple{Any,AbstractInfUnitRange{Int}}}) = $Typ() # no way to lose const rows
         applybroadcaststyle(::Type{<:AbstractMatrix}, ::$Typ) = LazyArrayStyle{2}()
+        applybroadcaststyle(::Type{<:ApplyMatrix{<:Any, <:Any, Args}}, ::$Typ) where {Args<:Tuple} = LazyArrayStyle{2}() # ambiguity
         applylayout(::Type, ::$Typ, _...) = LazyLayout()
     end
 end
diff --git a/test/test_infbanded.jl b/test/test_infbanded.jl
index a632a3a..331e263 100644
--- a/test/test_infbanded.jl
+++ b/test/test_infbanded.jl
@@ -4,7 +4,8 @@ import InfiniteArrays: TridiagonalToeplitzLayout, BidiagonalToeplitzLayout, TriP
                         TriToeplitz, ConstRows, SymTriPertToeplitz, AdjTriPertToeplitz, subdiagonalconstant,
                         diagonalconstant, supdiagonalconstant, PertTridiagonalToeplitzLayout
 using Base: oneto
-using LazyArrays: simplifiable, ApplyLayout, BroadcastBandedLayout, islazy
+using LazyArrays: simplifiable, ApplyLayout, CachedArrayStyle, LazyArrayStyle, BroadcastBandedLayout, islazy
+import Base.Broadcast: BroadcastStyle
 
 const InfiniteArraysBandedMatricesExt = Base.get_extension(InfiniteArrays, :InfiniteArraysBandedMatricesExt)
 const InfToeplitz = InfiniteArraysBandedMatricesExt.InfToeplitz
@@ -40,6 +41,7 @@ const InfBandCartesianIndices = InfiniteArraysBandedMatricesExt.InfBandCartesian
         @test (B*A*x)[1:10] == [0; 10; 14; 12; zeros(6)]
 
         @test _BandedMatrix((1:∞)', ∞, -1, 1) isa BandedMatrix
+
     end
 
     @testset "∞-Toeplitz" begin
@@ -380,4 +382,13 @@ const InfBandCartesianIndices = InfiniteArraysBandedMatricesExt.InfBandCartesian
         A = BandedMatrix(1 => Fill(2im,∞), 2 => Fill(-1,∞), 3 => Fill(2,∞), -2 => Fill(-4,∞), -3 => Fill(-2im,∞))
         @test copy(Base.broadcasted(BandedMatrices.BandedStyle(), exp,A))[1:10,1:10] == exp.(A[1:10,1:10])
     end
+
+    @testset "BroadcastStyle with InfBandCartesianIndices" begin
+        A = BandedMatrix(1 => Fill(2im,∞), 2 => Fill(-1,∞), 3 => Fill(2,∞), -2 => Fill(-4,∞), -3 => Fill(-2im,∞))
+        B = view(A, band(0)) 
+        @test BroadcastStyle(typeof(B)) == LazyArrayStyle{1}()
+        A = BandedMatrix(1 => Fill(2im,∞), 2 => cache(Fill(-1,∞)), 3 => Fill(2,∞), -2 => Fill(-4,∞), -3 => Fill(-2im,∞))
+        B = view(A, band(0))
+        @test BroadcastStyle(typeof(B)) == CachedArrayStyle{1}()
+    end
 end